BR112016013655B1 - METHOD AND DEVICE FOR DATA SIGNAL RESOLUTION - Google Patents

Abstract

METHOD AND APPARATUS FOR RESOLVING DATA SIGNALS A method and apparatus for resolving individual signals into detector output data is disclosed. One aspect of the invention includes a processing circuit configured to receive detector output data, wherein the detector output data may be scaled data or unscaled data; transforming the detector output data to produce the scaled data wherein the detector output data is received as unscheduled data; detecting at least one signal at least partially based on the scaled data; and estimating a parameter associated with the signal, wherein the parameter estimation may preferably comprise an estimate of the signal power or time of arrival signal associated with the signal.

Description

BACKGROUND OF THE INVENTION Field of Invention

[0001] The present invention generally relates to a method and apparatus for determining parameters of detector output data signals (typically noisy) for use, in particular, although not exclusively, for recovery from from a radiation detector, from data affected by pulse stacking.

Background

[0002] The precise detection and measurement of radiation, vibration or other types of energy is employed in many industries, including homeland security, scientific instrumentation, medical diagnostics, materials analysis, meteorology, cargo transportation and logistics, technology information and communication (ICT) and mineral processing. These and other industries use this detection and measurement to analyze materials, structures, products, information, signals or other specimens. Transmission-based imaging, spectroscopic analysis, or other modalities can be used to perform this analysis.

[0003] In mineral and oil exploration, well extraction techniques use gamma rays and neutrons to determine the content of underground rock and mineral deposits. Data on the porosity and density of rock formations can be determined from nuclear well drilling techniques, which are then used to help detect the presence of geological reservoirs and their contents (e.g. oil, gas or water) .

[0004] In freight transport and logistics, X-ray scanning is used not only to scan cargo for security purposes (i.e. detection of illicit substances or explosives), but can also be used to measure weight, volume and distribution of cargo to determine prices and generate manifests.

[0005] Navigation and distance determination by sound (SONAR) can be used in navigating and locating objects within a body of water. Sonic Distance Detection and Determination (SODAR) can be used to measure the scattering of sound waves by atmospheric turbulence and, for example, to measure wind speed at various heights above the ground and the thermodynamic structure of the lower layer of the atmosphere. .

[0006] Ultrasound can be used for medical imaging or other purposes, such as forming images of fetuses, locating flaws and/or measuring the thickness of certain types of objects or conducting real-time location of objects (for example, in environments of manufacture).

Summary of the Invention

[0007] The present invention relates to a digital signal processing technique capable of accurately estimating, in real time, the parameters of incoming radiation detection events, allowing the recovery of information from stacked events.

[0008] According to a first aspect of the invention, there is provided a method and apparatus for resolving individual signals into detector output data. The method comprises: receiving output data from the detector; transforming the detector output data to produce scaled data; detecting at least one signal based at least partially on the scaled data; and estimating a parameter associated with the signal. The apparatus comprises a processing circuit configured to carry out the method steps.

[0009] According to a second aspect of the invention, there is provided a method and apparatus for resolving individual signals into detector output data. The method comprises: receiving output data from the scaled detector; detecting at least one signal based at least partially on the scaled data; and estimating a parameter associated with the signal. The apparatus in the second aspect also comprises a processing circuit configured to perform the method steps.

[0010] In some embodiments, the estimated parameter is one or more of a signal energy or a signal arrival time.

[0011] In some embodiments, the method further comprises: determining the amplitude of a signal in the scaled data at least partially based on the difference between an average value of the scaled data stream following the signal and an average value of the scaled data before the signal; and estimating the signal energy at least partially based on the amplitude of the signal.

[0012] It will be appreciated that it may not be possible to properly characterize all data (uncharacterized data is termed "corrupted data"); such corrupted data can optionally be rejected. As such, in some embodiments, the method further comprises: generating a model of the detector output data based at least partially on the estimated signal energy; determine the difference between the model and the detector output data; and rejecting parts of the model that differ from the detector output data by more than a threshold.

[0013] In an exemplary embodiment of the invention, the method includes creating a model of the detector output using the signal parameters in combination with the detector's impulse response. The method may include discarding energy estimates deemed not sufficiently accurate. In one embodiment, the method includes displaying all sufficiently accurate energy estimates in a histogram.

[0014] In some embodiments, where the detector output data comprises a plurality of samples representing at least one signal, the method further comprises transforming the detector output data at least partially based on transforming the signal into a signal scaled, wherein transforming the signal into the transformed signal comprises: shaping the signal at least partially based on a rising edge variable and a falling edge variable; transforming the rising edge variable such that the rise time of the signal is substantially zero; and transforming the falling edge variable such that the signal falling time is substantially infinite.

Onde: p(t) é o sinal, A é a energia do sinal, a é a variável de borda de subida, e b é a variável de borda de descida.[0015] In some embodiments, the method further comprises modeling the signal at least partially based on a double exponential waveform, where the double exponential waveform is given by:

Where: p(t) is the signal, A is the signal energy, a is the rising edge variable, and b is the falling edge variable.

Onde: x(n) é o valor do fluxo de dados de entrada na amostra 'n' a, b determinam as bordas de subida e de descida da forma de sinal y(n) é o fluxo de dados escalonados, que pode exigir maior escalonamento.[0016] In some embodiments, the method further comprises performing the signal transformation by the following operation:

Where: x(n) is the input data stream value at sample 'n' a, b determine the rising and falling edges of the signal shape y(n) is the scaled data stream, which may require greater scaling.

[0017] In some embodiments, the method further comprises deleting at least one of the samples within a window around the rising edge of the signal.

[0018] In some embodiments, the method further comprises detecting the at least one signal by determining one or more detection metrics, wherein the one or more detection metrics are determined by fitting an expected signal shape in one or more sliding windows of samples on the scaled data, and estimating a parameter fit between the expected signal shape and the scaled data for each window; analyze one or more of the detection metrics; and determining whether there are any signals in the scaled data based on said analysis of one or more detection metrics.

[0019] In some embodiments, the method further comprises comparing one or more detection metrics to a threshold; or, modeling one or more detection metrics with a quadratic approximation applied to one or more sliding windows of the detection metric data and comparing quadratic coefficients of a plurality of sliding windows of the detection metric.

Onde: k é a amostra, x(k) é a métrica de detecção para a amostra k, b(k) é um segmento dos dados escalonados, centrado na amostra k, e A é o vetor da forma de sinal esperada centrada.[0020] In some embodiments, the method further comprises determining one or more detection metrics, based at least partially on a least squares fit of the expected signal shape to the scaled data, wherein the detection metrics are given per:

Where: k is the sample, x(k) is the detection metric for the k sample, b(k) is a segment of the scaled data, centered on the k sample, and A is the vector of the centered expected signal shape.

[0021] In some embodiments, the method further comprises incrementally updating one or more detection metrics, based at least partially on the previous detection metric, using addition, subtraction, and/or scaling.

[0022] In some embodiments, the method further comprises discarding signals that are separated from the at least one signal by less than a threshold number of samples.

[0023] In some embodiments, the method further comprises transforming the detector output data at least partially based on convolution of a finite impulse response (FIR) filter with the detector output data.

[0024] The method optionally comprises an evaluation of the variance of the energy estimates in the data and validation of the modeled data.

[0025] In some embodiments, the apparatus comprises a processing circuit configured to perform each of the method steps. In other embodiments, the apparatus comprises further means for carrying out the steps of the method.

[0026] The apparatus may comprise any suitable apparatus for which pulse stacking recovery is useful. For example, it could be a metal detector, a landmine detector, a medical imaging device, a mineral detection device, an oil well drilling device, an unexploded ordnance detector, a cargo screening device , an X-ray fluorescence apparatus or an X-ray diffraction apparatus. The apparatus of this aspect comprises a processor for receiving the data in digitized form, adapted to perform the signal processing method described above. The apparatus may include an analogue-to-digital converter (ADC) adapted to receive the data, convert the data into digitized form and send the digitized data to the processor. This is particularly useful where the detector outputs analogue data, but is unnecessary where the detector outputs digitized data.

[0027] The processor may, for example, comprise an array of field-programmable gates (or an array thereof), a digital signal processor (or an array thereof), or a combination of the two. The apparatus may include an analogue front end that includes the analogue-to-digital converter (ADC).

[0028] The apparatus may, for example, include an electronic computing device in data communication with the processor, for controlling the processor and for displaying an output from the processor. The apparatus may include a radiation detector.

[0029] It should be understood that the term "signal" is interchangeable in this context with "pulse", as it refers to the output corresponding to individual detection events rather than the overall output signal comprising the sum of individual signals. It will also be appreciated that the temporal position (or timing) of a signal can be measured or expressed in a number of ways, such as according to the time (or position on the time axis) of the signal maximum or the leading edge of the signal. This is usually described as the arrival time ("arrival time") or detection time.

[0030] It will also be understood that the term "detector data" refers to data originating from a detector, whether subsequently processed by associated or other electronics inside or outside the detector.

[0031] The invention is applicable to a wide range of implementations utilizing a variety of detector types and detector output data formats, which allow a range of outputs to be produced. For example, in one embodiment, the detector output data can be generated by an X-ray load screening apparatus comprising multiple LYSO detectors and the resolution of individual signals allows generation of a three-dimensional X-ray attenuation image of the passage object through the tracking device. In another embodiment, the detector output data can be generated by an energy dispersion spectroscopy detector in a scanning electron microscope, and the resolution of individual signals allows the assignment of each X-ray pulse measured at the detector to a compartment of energy into a spectral histogram, which can then undergo further software processing to determine the quantitative composition of the sample material.

[0032] Key metrics that are significant in industries to which the present invention is applicable include: • the input count rate (ICR) that can be handled by the technology; • technology throughput (ie, the ratio of the number of counts considered compared to the number of counts disregarded); • the best energy resolution achieved with the technology (at a low count rate); • energy resolution degradation with up-count rate; • the best energy resolution that can be achieved with very high output count rates; • peak position stability and peak resolution with the count rate; • the stability of peak position and peak resolution over time; • the detection of low energy pulses; • the dynamic range (ie, detection of both low-energy and high-energy events); and • the technology's ability to handle pulse shape variability.

[0033] It will be appreciated that various implementations of the present invention address one or more of these metrics providing inventive improvements over prior art signal processing methods.

[0034] Throughout this description (including any claims that follow), unless the context otherwise requires, the word "comprises" and variations such as "comprises" and "comprising" shall be understood to imply the inclusion of an integer or step or group of integers or steps, but not the deletion of any other integer or step or group of integers or steps.

Brief Description of the Drawings

[0035] In order that the invention may be more clearly determined, preferred embodiments will now be described, by way of exemplary implementations, with reference to the accompanying drawings, in which: Figure 1 illustrates an exemplary spectroscopic apparatus adapted to perform stack recovery of pulses according to one embodiment of the invention. Figure 2 is a schematic cross-sectional view of the Silicon Drift Diode (SDD) detector of Figure 1. Figure 3 is a graph illustrating approximately 100 µs of exemplary data emitted from a diode detector. of the type shown in Figure 2. Figure 4 illustrates an example of an X-ray microanalysis apparatus adapted to perform pulse stacking recovery in accordance with another embodiment of the present invention. Figure 5 is a schematic view of an electron microscope with the EDS system turned on that can be used in the X-ray microanalysis apparatus of Figure 4. Figure 6 illustrates an exemplary X-ray energy spectrum collected using an SDD detector configured to measure fluorescent X-rays emitted from a sample. Figure 7 is a schematic diagram of the functional elements of the spectroscopy apparatus of Figure 1. Figures 8a, 8b and 8c illustrate exemplary waveforms resulting from digitizing detector output data over time intervals of 1000 microseconds, 100 microseconds and 10 microseconds, respectively. Figures 9a, 9b and 9c illustrate exemplary forms of pulse stacking, namely: "tail-end stacking", "peak stacking" and "multi-peak stacking", respectively. Figure 10 illustrates an exemplary modeling of the signal detection process according to an embodiment of the invention. Figure 11 illustrates a more detailed mathematical model of the energy detection process shown in Figure 10. Figure 12 illustrates an exemplary process for determining a histogram illustrating parameters of detector data using a pulse shape transformation in accordance with one embodiment. Figure 13 illustrates an exemplary pulse shape for radiation received at a detector. Figures 14a and 14b depict an exemplary result of transforming detector impulse response data into scaled data (also called integral data) in the pulse shape transformation process. Figure 15 represents the rising edge of an exemplary transformed pulse. Figures 16a and 16b illustrate the performance of an example detection metric on data collected from an SDD detector. Figure 17 illustrates an exemplary process for validating a model detector output generated from pulse stack recovery processes in accordance with one embodiment of the invention. Figures 18a, 18b and 18c illustrate an example where a finite response filter is convoluted with embedded detector data. Figure 19 illustrates an exemplary graph of output count rate versus input count rate as the integration length and integration factor are varied in the pulse stack recovery process according to one embodiment. Figure 20 demonstrates an exemplary optimization of the full width of the main peak to half its maximum value (FWHM) that can be achieved by changing the number of suppressed samples in the pulse stack recovery process according to one embodiment. Figure 21 illustrates an exemplary pulse structure. Figure 22 depicts an exemplary matrix structure of (ATA) associated with the arrival of multiple pulses in detector data, for example, as depicted in Figure 16a, where the system matrix is represented by A. The matrix requiring inversion , (ATA), is a square matrix, where the number of rows equals the number of signals in a given data structure. Figure 23 represents the structure of the inverse of (ATA).

Detailed Description of the Preferred Embodiment

[0036] The advantages and features of the invention and the methods for carrying it out may be more readily understood by reference to the following detailed description of preferred embodiments and the accompanying drawings. The invention can, however, be embodied in many different forms and should not be construed as being limited to the embodiments set forth herein. Rather, these embodiments are disclosed so that this description is thorough and complete and fully conveys the concept of the invention to those skilled in the art, and the invention is only defined by the appended claims. Similar reference numbers refer to similar elements throughout the report.

[0037] The drawings and description must be considered illustrative and not restrictive in nature. Similar reference numbers designate similar elements throughout the report.

[0038] Furthermore, since the sizes and thicknesses of the constituent elements depicted in the accompanying drawings are arbitrarily given for better understanding and ease of description, the invention is not limited to the sizes and thicknesses illustrated.

[0039] Methods of medical diagnosis and treatment that depend on the detection and accurate measurement of radiation, vibration or other types of energy include flow cytometry, hematology, tumor immunology and chemotherapy, prenatal diagnosis, genetics, leukemia diagnosis, sequencing of genes and bone densitometry. In particular, single photon emission computed tomography (SPECT), positron emission tomography (PET), and X-ray computed tomography (X-ray CT) allow for advanced medical imaging.

[0040] Spectroscopy can be used to analyze materials. Knowledge about the material is obtained by analyzing the radiation emission or absorption of elements within the sample. This radiation emission may be stimulated emission due to some form of incidental radiation or the result of natural emission from the constituent elements.

[0041] Two techniques of stimulated emission spectroscopy are X-ray fluorescence (XRF) and particle-induced X-ray emission (PIXE). These examples are used in material analysis in the ICT and minerals exploration and processing industries. In these techniques, knowledge of the material is gained by detecting and analyzing secondary (or fluorescent) X-rays emitted from the material after the material has been energized by stimulation with high-energy photons or particles.

[0042] Gamma-ray spectroscopy, for example, is a form of spectroscopy in which the emitted electromagnetic radiation is in the form of gamma rays. In gamma-ray spectroscopy the detection of the resulting radiation can be performed with a scintillation crystal (such as thallium-activated sodium iodide, NaI(Tl)), although there are several other types of detectors that can also be used. NaI(Tl) crystals generate ultraviolet photons according to the incident gamma ray radiation. These photons can then be directed into a photomultiplier tube (PMT) which generates a corresponding electrical signal or pulse. As a result, the interaction between the photons and the detector gives rise to pulse-like signals, the shape of which is determined by the incident gamma-ray radiation, the detection crystal and the PMT. The fundamental form of these pulse-like signals is referred to as the detector's impulse response.

[0043] The output of the photomultiplier is an electrical signal that represents the sum of input signals, in a determined way, generated in response to discrete gamma rays arriving at the scintillation crystal. By examining the detector output over time, and in particular the amplitude of the component signals, it is possible to deduce information related to the chemical composition of the material.

[0044] Analysis by all of the above methods requires the characterization of the individual signals generated in response to incident radiation, vibration or other forms of energy. Signal parameters of particular interest include signal amplitude, number and time of occurrence, or temporal position (whether measured as arrival time, maximum time, or not). If the arrival times of two detected incident events vary by more than the detector response time, analysis of the detector output is relatively straightforward. However, in many applications, a high flow of incident events cannot be avoided, or it may be desirable so that the analysis can be performed in a reasonable amount of time. As the time between arrivals decreases, characterization of all resulting signals becomes difficult.

[0045] In particular, signal analysis is affected by a phenomenon known as pulse stacking [G.F. Knoll, Radiation Detection and Measurement, 3rd edition, chapter 17, pg. 632-634, 658 and 659, John Wiley and Sons, New York 2000], whereby multiple detected incident events arriving more or less simultaneously within the detector's temporal resolution time produce signals that come together and can be counted as a single signal. The detector does not have enough time to recover from the first detection (that is, for the signal to return to baseline) to accurately detect subsequent events.

[0046] The energy of an incident gamma ray or X-ray is reflected in the amplitude of the pulse-like signal produced by the detector. The presence of specific energies within the detector signal is indicative of particular elements in the material from which the gamma rays or X-rays arrived. Thus, failure to differentiate a large amplitude signal caused by a single scintillation event from the superposition of multiple events can have a serious effect on the accuracy of subsequent spectroscopic analysis.

[0047] Analog pulse shaping circuits (ie pulse shape amplifiers, delay line circuits and discriminators) can be used to analyze the output of radiation detectors. However, it may be desirable to use direct digitization of the detector output followed by digital pulse analysis techniques. In designing and implementing optimal filtering techniques for digital pulse processing, the approach to dealing with pulse stacking at the output of radiation detectors can be consistent for both digital and analog systems.

[0048] Certain pulse-shape electronics can reduce the detector response time, resulting in a decrease in the prevalence of stacking in the final spectrum [A.Pullia, A. Geraci and G. Ripamonti, Quasioptimum Y and X-Ray Spectroscopy based on Real-Time Digital Techniques, Nucl. Inst. and Meth. A 439 (2000) 378-384]. This technique is typically limited, however, by the detector's response time.

[0049] Another approach is "pulse stacking rejection", which uses fast digital filters and logic circuits to detect stacked events and discard corrupted data. Pulse stack-free signals are used in the analysis. However, as the rate of radiation incident on the detector increases, so does the probability that pulse stacking will occur, and the more it is necessary to discard data. Consequently, pulse stacking rejection is of limited usefulness once a state is quickly reached beyond which an upper incident radiation flux ceases to reduce the time required for spectroscopic analysis, as an increasing percentage of data has to be rejected. In many applications, as much as 80% of the information can be lost to the effects of dead time and pulse stacking [DM Scates and JK Hartwell, Appl. Radiat. Isot. 63, 465-473 (2005)].

[0050] A more sophisticated approach is to make use of knowledge about the profile of a single detector pulse or mathematically model the parameters of a signal. It is then possible, in principle, to distinguish the signals or impulses that originate from a single event from those caused by the stacking of pulses. In one such analysis method [RJ Komar and H.-B.Mak, Digital Signal Processing for BGO Detectors, Nucl. Inst. and Meth. A336 (1993) 246-252], the signals that depart from the simple profile are selected for further analysis. This analysis involves fitting, through an iterative process, two pulses of varying separation and amplitude. Once the fit is determined, the characteristics of the individual pulses are known from the fit parameters and therefore a pulse coming from two nearby signals can be decomposed into the corresponding discrete signals. However, this approach cannot accommodate circumstances where pulse stacking is caused by the superposition of more than two signals. Iterative optimization is computationally expensive and the time taken to perform this procedure makes it impractical in most situations.

[0051] Pulse stacking is also a problem in seismic data collection; Naoki Saito (in Super resolution of Noisy Band-Limited Data Adaptive Regularization and its Application to Seismic Trace Inversion, CH2847-2/90/0000-123, 1990) refers to the resolution of closely placed peaks in a seismic trace. This technique can employ adaptive data regularization to recover missing frequency information in the presence of noise and, through repeated iterations, obtain better resolution. However, this approach is computationally intensive.

[0052] There is interest in implementing more complex signal processing methodologies to further improve detector resolution, timing and processing rate at high count rates [R. Novak and M. Venclj, IEEE Trans. nucl. Know. 56(6), 3680-3687 (2009)]. However, the performance of more advanced "ideal" digital pulse processing techniques depends heavily on the assumptions underlying such techniques [S. Riboldi, R. Abbiati, A. Geraci and E. Gatti, IEEE Trans. nucl. Know. 52(4), 954-958 (2005)].

[0053] Methods that require a large computational effort can limit the maximum throughput and present challenges for the practical implementation of the processing technology in certain environments.

[0054] Figure 1 illustrates an exemplary spectroscopic apparatus adapted to perform pulse stacking recovery in accordance with one embodiment of the invention. In Figure 1, there is provided a spectroscopy apparatus adapted to perform pulse stacking recovery according to an exemplary embodiment of the present invention. The spectroscopy apparatus 100 includes a detector 110 in the form of a silicon-shunt diode (SDD) detector of a type used for detecting and measuring X-rays in energy dispersive X-ray spectrometry, a signal 114, a computer 116 for display, and cables 112 for coupling the output of the signal processing unit 114 to the computer 116.

[0055] Figure 2 is a schematic cross-sectional view of the silicon-shunt diode (SDD) detector 110 of Figure 1. The detector 110 is constructed of high-resistivity, high-purity n-type silicon 174, which is of the order 450 µm deep and has an active surface area of 10 to 150 mm2. The active area of the incident face 222 of the detector 110 (viz. the window side where X-ray radiation is normally incident during use) is covered by a thin junction 224 of homogeneous p-type silicon. Rear portion 280 of detector 110 (viz. device side) has p-type ring concentric shunt electrodes 282a, 282b with integrated voltage dividers (not shown).

[0056] A transverse electric potential field is created across the thickness of the detector 110 by an array of evenly spaced electrodes on its front and rear surfaces. Furthermore, a strong radial collection field is created by forming concentric ring electrode patterns 282a, 282b. These electrodes create a radial and transverse electric field to produce a "collection channel".

[0057] The X-rays 284 impinging upon and interacting within the detector 110 produce pairs of electron holes; the number of pairs created is proportional to the energy of the incident X-ray. Free electrons drift through detector 110 along a collection channel 286 defined by the electric potential field within detector 110 and are collected at a central electron collector anode 288. The electrical charge collected at central anode 288 is amplified, in a first stage amplification process, by a field effect transistor (FET) 190, integrated in detector 110. The signal emitted by anode 288 is then amplified and formed by a signal processing unit 114 as output data from detector scanned (see Figure 3).

[0058] A desirable benefit of the structure of the silicon bypass diode detector 110 is the low capacitance of the anode 288, resulting in low electronic noise. This allows for better energy resolution and higher count rates than some other X-ray detectors such as Si-PIN photodiodes or Si(Li) crystals.

[0059] Figure 3 is a graph illustrating approximately 100 μs of sample data emitted from a silicon shunt diode detector of the type shown in Figure 2. The charge collected at anode 188 was amplified and shaped by amplification electronics and pulse shaping, as discussed above; Figure 3 illustrates the resulting signal. The shape of the signal that results from the detection of a single X-ray is evident in this detector output digitized at 300. However, there are circumstances in which multiple X-ray events will interact with the detector in rapid succession. In such circumstances, evident at 302a, 302b, detector 110 does not recover from an event (ie, the signal does not return to baseline) before the next event occurs, leading to pulse stacking. It should be noted, therefore, that spectroscopy apparatus 100 is susceptible to pulse stacking, whereby signal processing unit 114 is used as described above to determine the location and amplitude of pulses at the output of detector 110.

[0060] In some exemplary implementations, the spectroscopy apparatus takes several different forms depending on the implementation, for example, a metal detector, a land mine detector, an imaging apparatus (such as an imaging apparatus medical), a mineral detection apparatus, an oil well, a luggage screening apparatus, an X-ray fluorescence apparatus, an X-ray diffraction apparatus, an X-ray absorption spectroscopy apparatus , an X-ray backscatter apparatus, a small angle neutron scattering apparatus, a powder diffractometer apparatus, a neutron reflectometer apparatus, an oil extraction apparatus, a scanning electron microscope apparatus, a semiconductor radiation (such as a silicon drift detector, a cadmium-zinc telluride detector, or a high purity germanium (HPGe) detector), a vibration detector such as a seismic reflection apparatus, a radio detection and telemetry (RADAR) apparatus, a sound navigation and telemetry (SONAR) apparatus, an element detection and measurement apparatus, a radiation safety detection apparatus, a biological testing apparatus (such as a flow cyclometry apparatus or a radioimmunoassay) or a superconducting apparatus (such as a superconducting tunnel junction apparatus or a superconducting calorimeter).

[0061] In accordance with one embodiment of the present invention, Figure 4 depicts an exemplary X-ray microanalysis apparatus adapted to perform pulse stacking recovery in accordance with another embodiment of the present invention, shown schematically at 410. X-ray microanalysis 410 includes a detector in the form of an electron microscope 412 (with integrated Energy Dispersive Spectrometry (EDS) system 414), a signal processing unit 404 (comparable to that of Figure 1), a computer 406 for display and cables 402 for coupling the output of signal processing unit 404 to computer 406. Signal processing unit 404 determines the location and amplitude of pulses at the output of electron microscope 412, as described above.

[0062] Figure 5 is a schematic view of an example electron microscope 412 with an integrated EDS system 514 that can be used in the X-ray microanalysis apparatus of Figure 4. An electron gun 520 can produce an electron beam , which is focused by a pair of successive condenser lenses 522a, 522b. The resulting focused electron beam 524 passes through an aperture 526 in a vacuum chamber 528 of the electron microscope, which electron beam 524 collides with a specimen 530 mounted on a stage 532 within the chamber 528. The focused electron beam 524 may be scanned through specimen 530 using sweep coils 584.

[0063] When electron beam 524 collides with specimen 530, electrons are ejected from specimen 530, leading to a cascade of electrons from higher to lower orbital energy and the emission of X-rays. These X-rays have wavelengths unique to the elements that make up 530 specimens, so they can be used to characterize the elements.

[0064] The analysis of emitted X-rays begins with the EDS system 514, which is mounted outside the electron microscope 412. The EDS system 514 comprises a silicon-shunt diode (SDS) detector 536, connected to the end of a finger cool finger 538. Cool finger 538 is used to cool the detector surface 536 to -25°C in some implementations. The output signal from SDD detector 536 is amplified and processed by pulse forming electronics (not shown) housed in body 540 of EDS system 514. Ultimately, the energy of the fluorescent X-rays is determined by the processing unit of signal 404. The EDS system 514 is mounted on an automated variable motion stage 542 to allow automated control over the distance between the SDD detector 536 and specimens 530.

[0065] Figure 3 illustrates the digital time series formed from X-rays emitted from the EDS system 514 and captured by the silicon-shunt diode (DDS) detector 536. The area under the individual pulses 300 defines the energy deposited in the detector by the emitted X-rays.

[0066] Figure 6 illustrates an exemplary X-ray energy spectrum, collected using an SDD detector (cf. Figures 2, 4 and 5) configured to measure fluorescent X-rays emitted from a sample. An X-ray tube can stimulate the emission of fluorescent X-rays. The relative energy of fluorescent X-rays is indicated along the X-axis; the total number of energy channels in this spectrum is 8,192 channels. The Y axis indicates on a logarithmic scale the number of signals recorded in each energy channel.

[0067] The spectrum in figure 6 represents a total data collection of 60 seconds; the input count rate (ICR) of the SDD detector (the number of events that interact with the detector each second) was about 153,200 events per second. The SDD detector's output count rate (OCR) (the number of events leaving the EDS system each second) was approximately 131,700 events per second; system dead time (the difference between ICR and OCR) was 14%. The energy resolution of this X-ray spectrum, defined as the full width of the main peak at half its maximum value (FWHM), was 159 electron volts (eV) or 2.48%.

[0068] The most common X-ray fluorescence from naturally occurring iron (which is predominantly 55Fe) has an energy of 6.40 keV. In the energy spectrum of Figure 6, this X-ray emission peak is shown at 650, at approximately channel 2550. Another X-ray fluorescence known to be characteristic of 55Fe is the emission peak at 7.06 keV, visible at 652 in the X-ray energy spectrum of Figure 6. Less common X-ray fluorescence from other elements in the sample (or ambient air) can also be seen in the energy spectrum at 654.

[0069] Two additional, distinct peaks are visible (at 656 and 658) between channels 5000 and 5500. These peaks are not due to high energy X-ray fluorescence, but rather to the superimposition of signals from the characteristic lower energy peaks of 55Fe at 6.40 keV and 7.06 keV (at 650 and 652) , respectively. The superposition of these peaks, due to pulse stacking, occurs at the output of the SDD detector, when radiation events arrive at the detector in such rapid succession that the detector cannot adequately recover from the first event (the detector output signal does not return to the baseline) before the arrival of the subsequent signal.

[0070] Pulse stacking in the digitized output of an SDD detector causes stacking peaks in the X-ray energy spectrum these peaks can interfere with the accurate characterization of materials as they can mask spectral peaks from other X-ray fluorescence X originating from the sample. Thus, signal processing unit 114 is employed as described above to determine the location and amplitude of pulses at the output of the SDD detector.

[0071] The approach of the present invention can be applied in many other fields. In some implementations, pulse stacking is a problem when processing seismic data. Some approaches are computationally intensive (even if they produce good results); the method of the present invention can be applied to the processing of seismic data, without excessive computational overhead in such a way that a relatively fast and cheap alternative approach is provided, even if in some applications the results are not as good as are provided by some techniques.

[0072] In another embodiment of the invention, a reflection seismology system is used to employ sonic energy to perform underground oil exploration as a non-limiting example. Sonic reflection, or reflection seismology, is a technique for geophysical exploration using the principles of seismology to determine the properties of the subsurface environment. Reflection seismology is conducted by initiating seismic waves underground at an initiation point using a blast, vibrators or specially designed air cannon. The seismic waves thus generated are a type of elastic wave that is carried through the Earth. Different types of subsurface material below, such as granite, shale, gas or oil, have different acoustic impedances so when the initiated seismic waves find a boundary between materials (that is, between materials and with different acoustic impedances), some of the wave energy will be transmitted across the boundary, and a portion of the wave energy will be reflected off the boundary. The amplitude of the reflected wave depends on the magnitude of the wave arriving at the boundary, the angle at which the wave crosses the boundary, and the impedance contrast between the two materials.

[0073] The portion of the seismic wave that is reflected back from the boundary to the earth's surface is detected by a seismometer assembly. The seismometer assembly comprises a plurality of individual geophones that convert ground motion induced by reflected seismic waves into electrical signals. In use, the geophones are attached to the Earth's surface, and connected together with cables. The electrical signals emitted by the geophones are then recorded in a recording station, for later analysis and processing. The recording station includes a pulse processing board comparable to the pulse processing board 114 of Figure 1, adapted to receive and process the electrical signals emitted by the geophones, to resolve the individual signals at the geophones output.

[0074] It should be noted that, in some applications of this technique, there may be a single detonation point with multiple sonic detectors for recording the reflected seismic waveforms. In other applications, multiple blast sites can be used in conjunction with a multiplicity of sonic detection sites to determine a more robust model of the subsurface environment.

[0075] A similar system according to another embodiment of the present invention can be used for conducting exploration studies in the marine environment. In this embodiment, the system comprises a vessel towing a series of pneumatic air guns as an excitation source. These guns emit low-frequency sound pulses (up to 300 Hz and 250 dB) into the ocean to stimulate seismic waves in the sea floor below. The system also includes several seismic cables to detect the reflected seismic waves; the cables which are typically implemented in parallel are, in this embodiment, at least 6 km in length and are spaced 150 meters apart, and provided with hydrophones at regular intervals along each cable to record the reflected characteristics of the sound signals under the seabed. The system, in accordance with this embodiment, includes a pulse processing board (on the ship) comparable to the pulse processing board (114) of Figure 1 for receiving and processing the output of the hydrophones in order to resolve the individual signals in the output of these hydrophones.

[0076] Reflection seismology is the main form of exploration for hydrocarbons in both terrestrial and marine environments and can be used to find other resources including coal, ores, minerals and geothermal energy. For more detection of shallow subsurface features, up to a few tens of meters deep, electromagnetic waves can be used instead of elastic waves, a technique called ground-penetrating radar. All of these systems may, in accordance with other embodiments of the present invention, include a pulse processing board comparable to the pulse processing board 114 of Figure 1 for processing the output of the sonic or radar detectors in order to resolve the individual signals. at the output of the respective detectors.

[0077] The method of the present invention can also be employed in many fields of material or product analysis. In some implementations, semiconductor processing and fabrication employs high-resolution measurement devices and techniques for evaluating sample parameters; various measurements are carried out in which thin films - such as oxides, metals or dielectrics - are deposited on semiconductor substrates of, for example, silicon. Non-destructive techniques are particularly useful for assessing thickness, identifying impurities and determining the refractive index of films to ensure high yields during manufacturing. One type of data that is particularly useful in the manufacture of semiconductors concerns the dosage and ion implantation profile of dopants such as arsenic, phosphorus and boron; these data can be obtained with X-ray fluorescence measurements taken at different small angles, and collected using an energy dispersive solid state detector, such as a Si(Li) detector. The method of the present invention can be used to process the output of such a detector in this field.

[0078] In automated sequencing of deoxyribonucleic acid (DNA), the problem of pulse stacking (and therefore dead time) can be avoided by ensuring that only one nucleotide is present in a detection region at any given time. However, the need to do so should be substantially reduced - allowing much faster data collection - by using the method of the present invention.

[0079] Likewise, the widespread use of miniaturized electronic circuits creates the need for sophisticated analysis techniques capable of performing high resolution measurement. In some implementations, photoluminescence lifetime spectroscopy is used to measure photoluminescence in semiconductors, especially those from compounds such as gallium arsenide that are susceptible to the incidence of structural discontinuities due to local crystallization defects. In another application, such defects are detected as variations in the photoluminescent output, measured with Single Photon Avalanche Diode (SPAD) detectors. The output of such detectors is processed to allow measurement of the lifetime delay photoluminescence characteristics of the sample under inspection. In some implementations, the rapid decay of photoluminescence on GaAs substrates allows the use of high repetition rate pulsed laser sources, theoretically allowing a data collection rate of 500,000 counts per second. In practice, pulse stacking limits the maximum data collection rate in such applications to about 100,000 counts per second due to the finite conversion dead time of the even faster commercially available time-to-span converter. The method of the present invention used to process data from such detectors will allow for significantly higher data collection rates in these applications.

[0080] The person skilled in the art will readily appreciate that the above-described radiation detector arrangement is merely an exemplary embodiment. The present invention can be equally applied to any system for detecting radiation, vibration or other types of energy, for example, as described herein.

[0081] In some implementations, other miscellaneous provisions to which the present invention is applicable, but not limited, include: 1) The detection of radiation with a number of other types of organic or inorganic scintillators, for example, but not limited to , barium fluoride (BaF2), calcium fluoride (CaF2), bismuth germanate (BGO), cadmium tungstate (CdWO4), cesium iodide CsI, or thallium-doped CsI(Tl), sodium-doped CsI(Na) . Gadolinium oxysulfate (Gd2O2S), lanthanum bromide (Labr3), lanthanum chloride (LaCl3), lead tungstate (PbWO4), lutetium iodide (LuI3), lutetium oxyorthosilicate (LSO), sodium iodide doped with thallium NaI (Tl), yttrium aluminum garnet (YAG), zinc sulfide (ZnS), zinc tungstate (ZnWO4). 2) Radiation detection with solid-state (semiconductor) detectors that rely on detection of charge carriers (electrons and holes) generated in semiconductors from energy deposited by gamma-ray photons. For example, detectors made of silicon and germanium doped with lithium, cadmium telluride or cadmium zinc telluride. 3) Detection of electrons in scanning electron microscopy (SEM). Two types of electron detector can be used for SEM imaging: scintillator-type detectors (Everhart-Thornley) are used for secondary electron imaging, where the detector is charged with a positive voltage to draw electrons into the detector for better signal-to-noise ratio, while backscattered electron detectors can be either a scintillator or a solid-state detector. 4) Optical radiation detection in flow cytometry. In flow cytometry, detectors typically include silicon photodiodes or photomultiplier tubes (PMTs). Silicon photodiodes can be used to measure forward scatter when the optical signal is strong. PMTs are more sensitive instruments and are ideal for scattering and fluorescence readings.

[0082] Figure 7 is a schematic diagram of the functional elements of the spectroscopy apparatus of Figure 1, and is provided to explain in more detail the signal processing method for pulse stacking recovery employed by the apparatus of Figure 1. With reference 7, the radiation detector (750) is connected to a pulse processing board (752) through an analog front end (AFE) (754). The purpose of the AFE (754) is to digitize the signal produced by the radiation detector (750) by performing analogue to digital conversion, in this embodiment, at 125 MHz with 12-bit conversion precision.

[0083] Once the radiation output has been digitized by the AFE (754), the signal processing method for pulse stacking recovery is implemented. The digital signal produced by the AFE (754) is passed to the pulse processing Field Programmable Gate Array (FPGA) array (756). The pulse processing FPGA (756) then implements the pulse processing method of the present embodiment; a digital signal processing (DSP) coprocessor (758) may be used to assist the pulse processing FPGA (756) to implement the pulse processing method. Variables required by the pulse processing FPGA (756) and the data produced in the intermediate steps of the pulse processing method are stored in memory (760). Signal processing is controlled through a Data/Control Interface (762) which, in conjunction with a control processor (764), can be used to modify the execution of the signal processing. Output data from the signal processing method can be displayed on a display (766) via the Data/Control Interface (762). The display (766) is provided on a computer which may, if desired, be used to perform post-processing and control of the system.

[0084] Figures 8A, 8B and 8C illustrate the exemplary waveform resulting from digitizing detector output data at time intervals of 1000 microseconds, 100 microseconds and 10 microseconds, respectively. The various peaks in these values correspond to the detection of respective gamma rays. Some spikes appear as discrete signals or pulses (870, 872), which may indicate the presence of only a single gamma ray. Other peaks are due to stacking either two peaks (876) or three or more peaks (874).

[0085] Figures 9A, 9B and 9C illustrate exemplary pulse stacking forms, namely: 'tail-end stacking', 'peak stacking' and 'multi-peak stacking', respectively, according to an exemplary embodiment of the invention. As shown in Figures 9a, 9b and 9c, the effect of pulse stacking is shown by the illustrative signals or pulses represented as energy E versus time t (both in arbitrary units). Figure 9a illustrates so-called 'tail-end stacking' where, depending on the type of pulse conditioning employed, the tail (980) of a pulse (981) can provide a significant positive or negative offset (positive in the illustrated embodiment) to the amplitude of a subsequent pulse (982). Although the time offset between the two pulses, Δt, is relatively large (when compared to the total time interval for which the pulses prevail), the resulting signal envelope or waveform (984) is significantly above zero at moment of arrival of the second pulse (982).

[0086] The absence of a true null signal state between the two pulses corrupts the analysis as the tail of the first pulse falsely inflates the amplitude of the second pulse. Figure 9b illustrates the second form of pulse stacking, 'peak stacking'. Here two pulses (986) and (988) arrive closely spaced in time (ie, the shift time Δt between the pulses is small compared to the total time interval over which the pulses prevail). The resulting output waveform (990) appears more or less as a single pulse of slightly greater amplitude than any of the component pulses. In situations where the flow of events through the detector is extreme, it is not uncommon to have multiple events arrive within the detector response time leading to multiple peak stacking. One such case is illustrated by Figure 9c. Multiple signals or pulses (such as those shown at 992) arrive with random separation time Δt and sum to produce a resultant waveform (994) from which the parameters of the component signals are difficult to extract.

[0087] One of the components of the pulse stacking addressing method according to this embodiment is the estimation of certain parameters of the signals or pulses; these parameters are the number, arrival time, and energy of all gamma rays in the detector's data stream. These parameters are estimated, according to this embodiment, by mathematically modeling the signals in the data stream.

signal modeling

[0088] Figure 10 is a diagram illustrating exemplary modeling of the event detection process in accordance with an exemplary embodiment of the invention. Radiation or other events of energy g(t) (1000) are incident on the detector (1002) represented by the measurement process m(t), resulting in detector output data of y(t) (1004). The addition of a sampling process (1006) produces the digital detector data or 'time series' X[n] (1008).

[0089] It is possible to add to the model described above some knowledge about the physical processes of detection of energy events. Figure 11 illustrates a more detailed mathematical model of the energy sensing process shown in Figure 10 in accordance with an exemplary embodiment of the invention. The input to the g(t) detector is characterized by equation 1, where the g(t) input is assumed to be an unknown number (N) of delta function-type pulses of random amplitude (α) and time of arrival (T) . An exemplary implementation of such an entry is shown at (1110).

[0090] The detector is assumed to have a specific response to the input events, referred to as the detector impulse response d(t), which is illustrated in (1112). The digitized version of the detector's impulse response is denoted d[n].

[0091] The detector output is shown in (1116) and characterized by Equation 2, in which the detector output y(t) is the sum of a number of unknown signals of predetermined form d(t), with unknown energy ( α) and unknown arrival time (t). Consideration is given to random noise sources a(t) (1114). The digital detector data x[n] is shown in (1118) and is produced by the analog to digital converter.

onde d[n] é a forma de tempo discreto da forma predeterminada do sinal d(t), Δi é o atraso em amostras para o i-ésimo sinal, e új(n) é a forma tempo discreto do ruído. O sinal digitalizado x[n] também pode ser escrito na forma matricial como:

onde A é uma matriz m x N, as entradas das quais são dadas por:

[0092] The digitized signal x[n] at the output of the analogue to digital converter (306), as illustrated in (1118), is therefore given by: N

where d[n] is the discrete time form of the predetermined form of signal d(t), Δi is the delay in samples for the ith signal, and új(n) is the discrete time form of the noise. The digitized signal x[n] can also be written in matrix form as:

where A is an mxN matrix, the entries of which are given by:

[0093] Furthermore, T is the length of d[n] in samples, m is the total number of samples in the digitized signal x[n], α is the vector of N energies of the signals, and a is the noise vector in length m. The matrix A also

[0094] Thus, the columns of matrix A contain multiple versions of the signal format. For each of the individual columns the starting point of the signal shape is defined by the time position of the signal. In some implementations, if data signals arrive at positions 2, 40, 78 and 125, column 1 of matrix A will have '0' in the first row, the first signal shape reference point in the second row, the second reference point signal shape reference on the third line, etc. The second column will have '0' up to row 40, followed by the shape of the signal. The third column will have '0' until line 78; the fourth column will have '0' until row 125 and then the sign shape. Therefore, the size of matrix A is determined by the number of identified signals (which becomes the number of columns), while the number of rows depends on the number of samples in the 'time series'.

[0095] The signal processing method of the present embodiment therefore endeavors to provide an exact estimate of some unknown parameters of the detector data, including not only the number of component signals (N) at the detector output, but also the energy (α) and arrival time (T) of each of the component signals.

Pulse Shape Transformation

[0096] To date, pulse stacking rejection processing has involved using every form of the detector's impulse response to attempt to estimate the energies of individual pulses. As a result, the calculation involved the solution of a system of matrix equations, including the decomposition of an entire matrix (more or less) of dimension 45x45.

[0097] The present invention avoids the challenges of computation and application of prior art methods by first ensuring that the signal is already, or is transformed, into a simpler form for further processing, which substantially resembles a step function, in contrast to the curved peak waveform of typical detector data. This significantly reduces the computational burden of prior art methods and allows the processing of signals received at very high input count rates, and once processed, the output of signals with much higher output count rates.

[0098] The digital signal produced by the AFE is passed to the pulse processing field programmable gate array (FPGA) 756 which comprises a pulse shape transformer. Figure 12 illustrates an exemplary process for determining a histogram illustrating detector data parameters using a pulse shape transform in accordance with one embodiment. The steps illustrated in Figure 12 can be performed by a pulse processing FPGA 756, or any other component, such as a DSP coprocessor 758 and/or a control processor 764. In block 1220, pulse processing FPGA 756 processes detector data using a pulse shape transform to extend the pulse decay time to infinity. At block 1222, pulse processing FPGA 756 further processes data from detectors to detect the presence of pulses. At block 1224, pulse processing FPGA 756 calculates the energy and/or other parameters of interest from the detected pulses. At block 1226, pulse processing FPGA 756 verifies the accuracy of the estimates through a validation process described in detail below. Finally, at block 1228, pulse processing FPGA 756 uses the validated energy estimates to construct a histogram that can be used by the user for further post-processing.

[0099] Figure 13 represents an exemplary pulse shape for radiation received at a detector. As described earlier and with reference to Figure 13, the data stream contains pulses 1330 whose shapes are typically composed of a fast rising edge (1332), peaking (1334), then a more gradual falling edge which decays back to the baseline (1336). The pulse shape transformation module serves to compress the rising edge and extend the falling edge of each pulse in the time domain. Ideally, the rising edge would be compressed to become instantaneous, and the falling edge would be extended to infinity, however, the pulse shape characteristics of the detector will determine how close to this ideal can be achieved.

[0100] The pulse shape transformer is capable of transforming any number of a variety of pulse shapes to the desired step waveform with suitable transform operations, for example Gaussian or single exponential pulse shapes. However, the preferred embodiment described below models the signal pulses with a double exponential waveform that more closely represents the physical process of sensing events at the detector, providing the most sophisticated and accurate characterization of sensing events.

Implementation 1 - Double Exponential:

Onde: p(t) é o pulso, A é a energia do pulso, e a, b determinam as bordas de descida e subida da forma de pulso.[0101] An exemplary detector pulse shape, as shown in Figure 13, can be modeled by a double exponential waveform:

Where: p(t) is the pulse, A is the pulse energy, and a, b determine the falling and rising edges of the pulse shape.

Onde: x(n) é o valor fluxo de dados recebidos na amostra 'n' a, b determina as bordas de descida e subida da forma de pulso y(n) é o fluxo de dados escalonado, o que pode exigir escalonamento adicional.[0102] For a double exponential pulse shape, the Pulse Shape Transformer performs the following manipulation on the received data stream:

Where: x(n) is the received data stream value in sample 'n' a, b determines the falling and rising edges of the pulse shape y(n) is the scaled data stream, which may require additional scaling.

[0103] This can be performed with a standard infinite impulse response (IIR) filter structure.

[0104] The use of pulse shape transformation in the past was aimed at reducing the incidence of pulse stacking to improve throughput, typically when trying to isolate each individual pulse. In contrast, the result of extending the trailing edge to infinity as described above is that pulse stacking is significantly increased. For a given pulse, each pulse that arrives after it will be stacked after its infinitely long pulse response. Although this processing method therefore appears to be counterproductive and non-intuitive to a person skilled in the art, this intermediate processing step allows much simpler computational analysis of the detector data in the following processing stages when they are presented in this transformed state.

[0105] Figures 14a and 14b show an exemplary result of transforming the detector's impulse response data into scaled data (also called integral data) in the pulse shape transformation process.

Sample Suppression:

[0106] The transformation of the original pulse flow to the ideal step shape (by compressing the rising edge time to zero and extending the falling edge decay time to infinity) is not always possible to achieve, due to limitations modeling requirements, second-order effects, or limits on available resources for implementing the pulse shape transformation. In particular, Figure 15 depicts an exemplary rising edge of the transformed pulses occurring over several samples.

[0107] In order to obtain the advantage in computational reduction that the ideally transformed pulse shape would provide, the calculations can be slightly modified. A desirable modification ensures that the rising edge region of each pulse (where the actual transformed pulse data differs from the ideally transformed pulse) is excluded from the calculations. While the curved shape could theoretically be modeled, this would be computationally expensive, and as a more desirable option, excluding samples within a defined window around the rising edge avoids problems arising from unmodeled pulse rise time, and also any errors in the estimated time of arrival. If too many samples are excluded, stacking can become a new problem, and if too few samples are excluded, there may still be some pulse transition included in the calculation, leading to estimation errors. By eliminating these portions of the data stream, amplitude estimates can be performed as if the transformation had been ideal, while no degradation in the result is minor. If one or more events arrive during the excluded region of a first event, the excluded region is extended to cover all overlapping excluded regions of events in the cluster. Clustering is treated as a single event, but is flagged as stacking.

signal detection

[0108] The data from the transformed data stream is then analyzed for the presence of pulses. Detection of signals on a digitized detector waveform is achieved by fitting a "detection metric" model to a fixed number of data points. This fixed-length "detection window" is scrolled continuously through the digitized detector data. Detection window sizes can range from four to over 128 samples, however, the optimal window size is between four and 64 samples due to the usage costs of processing more than 64 samples.

[0109] Detection is implemented by performing a least squares fit of the expected pulse shape with one or more data sliding window segments. The term "sliding window" generally refers to an iterative process of performing mathematical calculations on finite-length segments (eg, windows) of the data. Mathematical calculations are sequentially performed on windows, and each window can overlap with adjacent windows. In some embodiments, two adjacent windows may differ by as little as one sample in their start and end points. In the present embodiment, the estimated parameter fit (at each window location) can be used as a detection metric.

Onde: x(k) representa a métrica de detecção para a amostra 'K'

ou seja, um segmento do fluxo de dados escalonado, centrado na amostra 'k' A é o vetor da forma de pulso esperada centrado.[0110] The least squares estimator to fit the expected pulse shape with the window segment is given by:

Where: x(k) represents the detection metric for sample 'K'

that is, a segment of the scaled data stream, centered on sample 'k' A is the vector of the centered expected pulse shape.

[0111] As a consequence of the previous pulse shape transformation process, the transformed pulse shape is closely approximated by a step function. Assuming that the pulse shape already exists, or that it has been transformed into an ideal step function, allows the computational load of the implementation to be significantly reduced, while only suffering a slight reduction in performance. If the expected pulse shape vector A is a near-zero step function of length 'N', for example:

[0112] Then, it can be observed that: the term (ATA)-1 is constant the term AT.b(k) is closely related to the term AT.b(k-1), and is given by:

[0113] Hence the least squares estimator for optimal pulse fit to the scaled data stream can be updated incrementally from the previous estimate using addition or subtraction and simple scaling.

[0114] The pulse detection metric is analyzed to determine the presence or absence of a pulse. In the case of no pulse present, the detection metric is simply zero significant noise. As a pulse enters the pulse detection metric window, the detection metric increases from zero and reaches a maximum when the pulse is centered in the window, dropping to zero as the pulse leaves the window. If multiple pulses are present in the window, the detection metric displays multiple peaks. There are two tests that are combined to detect the presence of a pulse: 1) The first test is a simple noise threshold test to eliminate false triggering due to noise. The detection metric is compared to a simple threshold. If the metric is less than the threshold, then no pulses are considered to be present. If it exceeds the threshold then one or more pulses may be present. The threshold is set to an adequate level to ensure that the probability of false triggering due to noise is acceptably low. The pulse processing FPGA 756 can determine the probability of false triggers based on, for example, the noise variance in the signal. When the pulse processing FPGA 756 sets the threshold based on variance, the probability can be adjusted to an acceptable level. 2) The second test is a search for significant peaks in the detection metric. This occurs when the slope of the peak changes from positive to negative. In the vicinity of a peak, the detection metric can be modeled by a quadratic approximation. A quadratic approximation is performed on a sliding window segment of the detection metric stream. A state machine can be used to monitor the squared coefficients to determine when the detection metric peaks. Further processing of the squared coefficients provides an estimate of the subsample arrival time of the pulse.

[0115] If tests indicate that a spike is present, and it is unlikely to have been caused by noise, then a signal detection event is declared. The location of the pulse in the scaled data stream is flagged, and transferred to the Energy Estimator.

[0116] The performance of the detection metric, in data collected from an SDD detector, is shown in Figures 16a and 16b. The detection metric responds quickly to the arrival of a new signal and decays back to the steady state value just after the rising edge of the X-ray has passed. The detection limit, for two pulses of similar size approaching each other is (NDW/2 - 1), where NDW is the length of the detection window in samples. Using an 8-sample detection window and a 60 Hz digitization rate can provide a pulse pair detection limit on the order of 50 ns.

[0117] The detection algorithm fits a quadratic model to a sliding window of five samples of the detection metric. In order for a peak to be declared, the algorithm analyzes the decomposition and declares a peak if the curvature is within an allowable range, the constant is above a threshold, and the linear term has changed from positive to negative. One embodiment uses five samples for the detection window, because this produces a particularly simple FPGA operation: with coefficients of (-2, -1,0,1,2) and (4,1,0,1,4) offset of bit, which is trivial on an FPGA, can be used. However, any number of samples can be chosen for the detection window.

Pulse Energy Estimation

Onde: b é um segmento do fluxo de dados escalonado A é uma matriz de sistema da forma acima descrita na Equação 6, cujas colunas contêm as formas de pulso, alinhadas com os locais de pulsos esperados, conforme determinado pelo processamento de detecção de pulsos, e x é a estimativa das amplitudes dos pulsos.[0118] The estimation of the amplitudes of a group of impulses (with or without accumulation) is performed by a least squares decomposition of a part of the data stream in steps according to the equation:

Where: b is a segment of the scaled data stream A is a system matrix of the form described above in Equation 6, whose columns contain the pulse shapes, aligned with the expected pulse locations, as determined by pulse detection processing, x is the estimate of the amplitudes of the pulses.

[0119] When the rising edge of the pulse has been compressed to time close to zero and the falling time of the pulse shape extends to infinity, the matrix of system A is of the form such that (AT.A )-1 is diagonal band with a narrow bandwidth, as shown in Figure 23. The stacking terms are largely decoupled from all but the immediate neighbor pulses. The non-zero terms of (AT.A)-1 can be determined analytically. This allows a significant reduction in computational load and implementation complexity.

[0120] The resulting amplitude estimate for a given pulse becomes equal to the mean value of the scaled data stream after the pulse has arrived (but before the next pulse), minus the mean value of the scaled data stream before the edge of rise of the pulse (but after the arrival of the previous pulse).

Accumulation Length:

[0121] There are advantages to limiting the number of samples included in the amplitude estimation calculation, rather than using the total length of data between a given pulse and its two immediate neighbors to estimate the pulse amplitude. Resolution degradation due to low frequency noise, DC drift and count rate is reduced by limiting the data used in an estimate to a maximum number of samples ("N") immediately on either side of a signal.

[0122] If a signal occurs closer than the 'N' samples on either side of the signal of interest, then the number of samples available for that portion of the calculation will be less than 'N'. In one embodiment, for a signal amplitude estimate to be considered acceptable it must be greater than a minimum number of samples included in the calculation. This ensures that the estimation variance due to noise has been reduced to a desired level. Pulses that come closest to the minimum threshold are discarded, in order to preserve the resolution of the output spectrum. This can have the effect of increasing dead time as the count rate increases.

[0123] Once the range estimates are made, further validation, rejection, formatting and presentation of the data can be performed.

Validation

[0124] The final phase of the real-time signal processing algorithm is the validation phase. In this phase all parameters that were estimated by previous algorithmic steps (pulse shape, number of events, arrival time and energy of events) are combined to reconstruct a "noiseless" model of the detector data. The 756 pulse processing FPGA builds the noise-free model by putting the calculated parameters into the model of the detector output y(t). For example, in one embodiment, the pulse processing FPGA 756 combines the detector impulse response d(t), the unknown energy (α) and unknown arrival time (T) to model the detector output y(t) through from equation (2). In another embodiment, the pulse processing FPGA 756 models the shape of the pulse detector response d(t) based on p(t) shown in equation (7), which the pulse processing FPGA 756 then models. substitutes into equation (2) to reconstruct the y(t) model. By subtracting this detector data model from the actual digitized detector time series, the pulse processing FPGA 756 can determine the accuracy of the estimated parameters. Much like looking at the residual from a straight-line fit of a data set, if the magnitude of the residuals is small, the parameters describe the data well. However, if at any point, large residuals are observed, the detector data has been misestimated and that portion of the data may be rejected.

[0125] The most common form of errors detected by the validation stage are errors in estimating the number of events in the data stream. When two events arrive < 50 ns apart they are logged as a single event. However, this error will cause a "blip" in the residual signal and misestimated events can be discarded. Spectrum Generation

[0126] Once the detector data processing is completed, the data is compiled into a histogram, representing the spectrum of estimated energies for all detection events identified in the data.

[0127] The method of the invention to estimate the variance compared to the underlying noise in order to accept or reject each detection event is the most accurate and controllable within the prior art methods. In some implementations, it is possible to rank all variance estimates from a particular data collection period and only use the best 80%. This sets the dead time to 20% and ensures that only the best guesses (for a given output) are used in the spectrum. By changing the variance or acceptable events, it is very simple to adjust the dead time and get an improved spectrum.

[0128] An important benefit of submitted processing in full space is the structure of the system matrix, A. The diagonal single-band nature of inv(ATA) (with a narrow bandwidth as shown in Figure 23) can allow inversion more accurate and/or robust via QR decomposition or single value decomposition (SVD). Alternatively, it may be possible to calculate the inverse and/or use the look-up tables once the shape, number and relative position of the events has been determined. This approach would be extremely hardware efficient.

[0129] An important benefit of performing the complete inversion of the SVD matrix is the ability to extract variance estimates, or 'degrees of confidence', about the energy of the X-rays being detected. The amplitudes of the entries in inv(ATA) are illustrative of the variance in the X-ray energy estimate. Events where the X-ray energy is known with greater confidence will have smaller entries in the diagonal range.

Advantages of Signal Processing

[0130] The implementation of this algorithm has a number of advantages, including: • a lower computational load, using the same hardware but to achieve more; • enable faster ADC sample rate or run multiple channels; • increased inbound and outbound count rates; • potential to detect very low energy events; • error bars in power estimates to help keep resolution constant; • enable better resolution/power rate performance, and; • address multiple shapes in large detectors.

Alternative Signal Processing Method

[0131] The embodiments described above represent a signal processing method according to the present invention. However, alternative methods can also be implemented that use concepts similar to those detailed in the above-described embodiments, with varied applications.

[0132] Within the initial data processing stage, a variant of the pulse transformation stage can be performed, which results in a similar scaled data output, albeit with more complex processing. Figure 17 illustrates an exemplary process for validating a model detector output generated from pulse stack recovery processes in accordance with one embodiment of the invention. A finite impulse response (FIR) filter is co-involved with the integrated detector data, as depicted in Figure 17. This operation can perform at least one of, and desirably both, the extent of the exponential decay of the input component. tail for a decay time of "infinity", and the compression of the rising edge component for a decay time of zero. This results in a much sharper edge over which accurate pulse arrival time estimates are obtained, and leads to the overall improvement in pulse energy estimation through accurate subsample arrival time estimation.

[0133] With reference to Figure 17, a process for generating a detector output model and validating the model will be described. In block 1702, ADC 1006 generates digitized data x[n] (see Figure 10 ). In block 1704, pulse processing FPGA 756 calibrates radiation detector 750. In block 1706, pulse processing FPGA 756 integrates the digitized data x[n]. At block 1708, pulse processing FPGA 756 wraps the integrated signal with a finite impulse response (FIR) filter in order to cancel out the tailing and rising edge components of the signal. At block 1710, pulse processing FPGA 756 locates the pulses using a detection metric to match a step wave to the integral data. In block 1712, pulse processing FPGA 756 estimates the energy and/or other parameters of interest of the detected pulses. At block 1714, pulse processing FPGA 756 computes a model based on the parameters and validates the model.

[0134] Processing data where either the drag exponent may have been extended to infinity, and/or the rising edge may have been compressed, leads to significant efficiency savings in matrix calculation compared to state methods of the technique. This method may have been brought about by trying to obtain the simplest possible pulse energy estimation algorithm, however, it may not be as efficient as in the embodiment described above.

[0135] For the instantaneous signal processing alternative, the following parameters can for example be varied to control the output data characteristics: 1) Integration Window: The maximum number of samples for which the energy is integrated. The integration window is reduced when the spacing between the pulses does not allow the complete window. 2) Integration Factor, which controls the maximum variance.

[0136] The maximum variance is defined for Integration Factor > = 1. The integration factor = 1, the maximum variance is 2/IntLength, and thus pulses are accepted only if the energy on either side of the rising edge can be integrated by exactly IntegrationLength samples. As the factor is increased, pulses for which the integration window is shorter can be included in the validated data. This increases the available output count rate, with a likely penalty in energy resolution, and also a penalty that is likely to vary with count rate - at higher count rate it is more likely that the pulses will be very close to reaching the specified maximum integration length.

[0137] Figure 18 shows exemplary waveforms formed at various stages of processing detector data pulses performed by pulse processing FPGA 756 in accordance with the present embodiment. Figure 18a illustrates exemplary output from pulse processing FPGA 756 at pulse integration block 1706. Figure 18b illustrates exemplary coefficients of a FIR filter used by pulse processing FPGA 756 at block 1708. Figure 18c illustrates exemplary output from pulse processing FPGA 756 at block 1708. Pulse processing FPGA 756 at block 1708 after pulse processing FPGA 756 convolves the integrated signal with the FIR filter coefficients of Fig. 18b. It can be seen that the processing sequence performed by the pulse processing FPGA 756 has the same effect as the rising edge compression, while extending from the falling edge to infinity.

[0138] Figure 19 shows an exemplary plot of the output count rate against the input count rate as the integration length and integration factor are varied in the pulse stacking recovery process according to one embodiment . There are at least two trends: as the integration length is increased, the available count rate decreases, and as the integration factor is increased, the available count rate increases.

[0139] It is noted that, even for moderate integration lengths, the dead time rapidly approaches 50%. This is a substantially worse result than if the integration length were not limited, and the deadtime was set to 10%. Furthermore, as the integration length increases, FWHM also increases (resulting in energy resolution degradation) and shift in peak location. This is significant as the length of integration can influence energy resolution but may require calibration to correct for peak offsets.

[0140] Regarding the integration factor, FWHM varies slightly as the integration factor increases from 1 to 1.5, allowing more pulses to be accepted. The result suggests that a factor greater than 1.0 should be considered to increase the available count rate without a drastic degradation in the FWHM.

[0141] Regarding the deletion of samples within a window defined around the rising edge, Figure 20 demonstrates an exemplary optimization of FWHM that can be achieved by changing the number of samples deleted in the pulse stacking recovery process of according to an embodiment. FWHM degradation is clear in the case of dropping four samples, so the ideal number for dropping is around six to ten. Above 10, there is no significant improvement in FWHM and the maximum available count rate degrades.

[0142] Both tail extension and rising edge compression are desirable for optimal processing to ensure maximum simplification of the signal approaching a step function; however, there are some situations where one or the other would not be essential. In some implementations, if the leading edge decays rapidly compared to the sampling rate - such as for a LYSO detector crystal, single exponential decay pulses, or slow ADC sampling rates - then leading edge compression may not be necessary. Likewise, for very slow decay pulses - such as detectors sitting in liquid nitrogen, or one with a very large capacitor - the decay tail will already be very long, and may not need to be extended to infinity given its similarity to a desirable pulse shape.

[0143] The cancellation of the vanishing exponent leads to an impulse shape approaching a step function, but a rise time governed by the pre-existing rise time of the detector and electronics. This can still be many dozens of samples, and lead to overlap. Figure 21 depicts an exemplary wrist structure. In this example, the rise time is of the order of 50 samples, which still leads to a significant possibility of pulse overlap and the inability to distinguish between stacked pulses. In this case, the ATA structure is illustrated in Figure 22. The data in each row to the left of the main diagonal is approximately constant, decreasing slightly on the diagonal, and then decreasing down the diagonal. However, in some implementations, when the pulses overlap (they are closer than about 50-60 samples), there are still many off-diagonal elements. The reverse ATA has a diagonal band structure illustrated in Figure 23, with a bandwidth on the order of 2-5 depending on how many pulses overlap.

[0144] It is convenient to describe the invention in relation to particularly preferred embodiments. However, the invention is applicable to a wide variety of implementations and it should be appreciated that other constructions and arrangements are also considered to fall within the scope of the invention. Various modifications, alterations, variations and/or additions to the construction and arrangements described herein are also considered to be within the scope and scope of the present invention.

[0145] Information and signals can be represented using any of a variety of different technologies and techniques. For example, data, instructions, commands, information, signals, bits, symbols, and chips that may be referenced throughout the above description may be represented by voltages, currents, electromagnetic waves, magnetic fields or particles, optical fields or particles, or any combination thereof.

[0146] The various illustrative logic blocks, modules, circuits, and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or combinations of both. To clearly illustrate this interchangeability of hardware and software, various illustrative components, blocks, modules, circuits, and steps have been described above, generally in terms of their functionality. Whether such functionality is implemented as hardware or software depends on specific application and design limitations imposed on the overall system. The described functionality can be implemented in several ways for each particular application, but such execution decisions should not be interpreted as a cause of departure from the scope of the embodiments of the invention.

[0147] The various illustrative blocks, modules, and circuits described in connection with the embodiments disclosed herein can be implemented or executed with a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC) , a field-programmable gate array (FPGA) or other programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. A general purpose processor may be a microprocessor, but, alternatively, the processor may be any conventional processor, controller, microcontroller, or conventional state machine. A processor can also be implemented as a combination of computing devices, for example a combination of a DSP and a microprocessor, a plurality of microprocessors, one or more microprocessors together with a DSP core, or any other type of configuration.

[0148] The steps of a method or algorithm and functions described in connection with the embodiments disclosed herein can be incorporated directly in hardware, in a software module executed by a processor, or in a combination of the two. If implemented in software, the functions may be stored in or transmitted through one or more instructions or code on a tangible, non-transient computer-readable medium. A software module can reside in random access memory (RAM), flash memory, read-only memory (ROM), electrically erasable ROM (EPROM), programmable and electrically erasable ROM (EEPROM), registers, hard disk, a removable disk , a CD-ROM, or any other form of storage medium known in the art. A storage medium is coupled to the processor so that the processor can read information from, and write information to, the storage medium. Alternatively, the storage medium may be an integral part of the processor. Disc as used herein includes compact disc (CD), laser disc, optical disc, digital versatile disc (DVD), floppy disk and Blu-ray disc where discs generally reproduce data magnetically while other discs reproduce data optically with lasers. . Combinations of the foregoing must also be included within the scope of computer-readable means. The processor and storage medium can reside in an ASIC. The ASIC can reside on a user terminal. Alternatively, the processor and storage medium may reside as discrete components in a user terminal.

[0149] For purposes of summarizing the disclosure, certain aspects, advantages and novel features of the invention have been described herein. It should be understood that not necessarily all such advantages can be achieved according to any particular embodiment of the invention. Thus, the invention can be embodied or carried out in a manner that achieves or optimizes an advantage or group of advantages as taught herein, without necessarily achieving other advantages as may be taught or suggested herein.

[0150] Various modifications of the embodiments described above will be evident, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments presented herein but is to be accorded the widest scope consistent with the principles and innovative features described herein.

Claims (15)

1. Apparatus for resolving individual signals (300, 870, 872, 1330) into detector output data, the detector output data comprising a stream of digital samples, each signal (300, 870, 872, 1330) being a pulse corresponding to an individual detection event occurring at a detector having a pulse shape with a rising edge and a falling edge above a baseline, and the detector output data originating from the detector, characterized in that it comprises: an analog front end (754) configured to perform analog to digital conversion of detector output data to obtain digitized detector output data; and a processing circuit configured to: transform the digitized detector output data such that the rising edge of each pulse is compressed and the falling edge of each pulse is extended, so as to produce digital scaled data comprising a stream transforming samples approaching an ideal step function and, following the transformation, performing pulse stacking recovery and detecting each signal (300, 870, 872, 1330) at least partially on the basis of the digital scaled data; and estimating one or more of a signal energy or a time of arrival of each signal (300, 870, 872, 1330) detected at least partially based on the digital scaled data. 2. Apparatus according to claim 1, characterized in that the processing circuit is further configured to: determine an amplitude of each signal (300, 870, 872, 1330) in the scaled data at least partially based on the difference between an average value of the scaled data samples following the signal (300, 870, 872, 1330) and an average value of the scaled data samples before the signal (300, 870, 872, 1330); and estimating each signal energy at least partially based on the amplitude of each signal (300, 870, 872, 1330), wherein the processing circuit is further configured to: generate a model of the detector output data at least partially based on each estimated signal energy; determine the difference between the model and the detector output data; and rejecting parts of the detector output data that differ from the model by more than a threshold. 3. Apparatus according to claim 1, characterized in that the step of transforming the detector output data comprises: modeling the pulse shape at least partially based on a rising edge variable and an edge variable of descent; transforming the rising edge variable such that the rise time of each signal (300, 870, 872, 1330) is substantially zero; and transform the falling edge variable such that the decay time of each signal (300, 870, 872, 133) is substantially infinite. 4. Apparatus according to claim 3, characterized in that the step of transforming the detector output signals further comprises modeling each pulse at least partially based on a double exponential waveform, in which the waveform double exponential is determined by:

where: P(t) is the pulse, A is the signal energy, a is the rising edge variable, and b is the falling edge variable. 5. Apparatus according to claim 3, characterized in that the step of transforming the detector output data is performed by the following operation:

where: x (n) is the value of the receiver output data stream received in sample 'n' 1. b determine the rising and falling edges of the signal shape y (n) corresponds to the scaled data, which may require more sizing. 6. Apparatus according to claim 5, characterized in that the processing circuit is further configured to delete at least one of the samples in the scaled data within a window around the rising edge of the signal (300, 870, 872, 1330); or wherein the step of detecting each signal (300, 870, 872, 1330) comprises: determining one or more detection metrics, wherein the one or more detection metrics are determined by adjusting an expected signal shape to a or more sliding windows of samples in the scaled data, and estimating a parameter fit between the expected signal shape and the scaled data for each window; analyze one or more of the detection metrics; and determining whether signals (300, 870, 872, 1330) exist in the scaled data based on said analysis of one or more detection metrics; or wherein the step of detecting each signal (300, 870, 872, 1330) comprises: determining one or more detection metrics, wherein the one or more detection metrics are determined by adjusting an expected signal shape to a or more sliding windows of samples in the scaled data, and estimating a parameter fit between the expected signal shape and the scaled data for each window; analyze one or more of the detection metrics; and determining whether signals (300, 870, 872, 1330) exist in the scaled data based on said analysis of one or more detection metrics; and wherein the step of analyzing the one or more detection metrics comprises: comparing the one or more detection metrics to a threshold; or modeling one or more detection metrics with a quadratic approximation applied to one or more sliding windows of the detection metric data, and comparing the quadratic coefficients of a plurality of sliding windows of the detection metric; or wherein the step of detecting each signal (300, 870, 872, 1330) comprises: determining one or more detection metrics, wherein the one or more detection metrics are determined by adjusting an expected signal shape to a or more sliding windows of samples in the scaled data, and estimating a parameter fit between the expected signal shape and the scaled data for each window; analyze one or more of the detection metrics; and determining whether signals (300, 870, 872, 1330) exist in the scaled data based on said analysis of one or more detection metrics; and wherein the step of determining the one or more detection metrics is at least partially based on a least squares fit of the expected signal shape to the scaled data, wherein the detection metrics are given by:

where: k is the sample, x (k) represents the detection metric for the K sample, b (k) is a scaled data segment, centered on the K sample, and A is the vector of the centered expected signal shape; or wherein the step of detecting each signal (300, 870, 872, 1330) comprises: determining one or more detection metrics, wherein the one or more detection metrics are determined by adjusting an expected signal shape to a or more sliding windows of samples in the scaled data, and estimating a parameter fit between the expected signal shape and the scaled data for each window; analyze one or more of the detection metrics; and determining whether signals (300, 870, 872, 1330) exist in the scaled data based on said analysis of one or more detection metrics; and incrementally updating one or more detection metrics at least partially based on the previous detection metric using addition, subtraction and/or scaling. 7. Apparatus according to claim 1, characterized in that the processing circuit is further configured to discard signals that are separated from the at least one signal (300, 870, 872, 1330) in the data scaled by less than a limited number of samples; or the processing circuit is further configured to transform the detector output data at least partially based on the convolution of a finite impulse response (FIR) filter with the detector output data. 8. Method for resolving individual signals (300, 870, 872, 1330) into detector output data, the detector output data comprising a stream of digital samples, each signal (300, 870, 872, 1330) being a pulse corresponding to an individual detection event occurring at a detector having a pulse shape with a rising edge and a falling edge above a baseline, and the detector output data originating from the detector, characterized in that it comprises: performing analog to digital conversion of detector output data using an analog front end (754) to obtain digitized detector output data; transform the digitized detector output data such that the rising edge of each pulse is compressed and the falling edge of each pulse is extended, so as to produce digital scaled data comprising a transformed stream of samples approaching a ideal step function, and successively transform, perform pulse stacking recovery and detect each signal (300, 870, 872, 1330) at least partially based on digital scaled data; and estimating one or more of a signal energy or a time of arrival of each signal (300, 870, 872, 1330) detected at least partially based on the digital scaled data. 9. Method, according to claim 8, characterized in that it further comprises: determining an amplitude of each signal (300, 870, 872, 1330) in the scaled data at least partially, based on the difference between an average value of the scaled data samples following the signal (300, 870, 872, 1330) and an average value of the scaled data samples before the signal (300, 870, 872, 1330); and estimating each signal energy at least partially based on the amplitude of each signal (300, 870, 872, 1330); or wherein the method further comprises: generating a model of the detector output data at least partially based on each estimated signal energy; determine the difference between the model and the detector output data; and rejecting parts of the detector output data that differ from the model by more than a threshold; or wherein the step of transforming the detector output data comprises: modeling the pulse shape at least partially based on a rising edge variable and a falling edge variable; transforming the rising edge variable such that the rise time of each signal (300, 870, 872, 1330) is substantially zero; and transforming the falling edge variable such that the decay time of each signal (300, 870, 872, 133) is substantially infinite; or wherein the method further comprises: deleting at least one sample in the scaled data within a defined window around the rising edge of the signal (300, 870, 872, 1330); or wherein the step of detecting each signal (300, 870, 872, 1330) comprises: determining one or more detection metrics, wherein the one or more detection metrics are determined by fitting an expected signal shape to a or more sliding windows of samples on the scaled data and estimating a parameter fit between the expected signal shape and the scaled data for each window; analyze one or more of the detection metrics; and determining whether signals (300, 870, 872, 1330) exist in the scaled data based on said analysis of one or more of the detection metrics. 10. Method, according to claim 8, characterized in that the step of detecting each signal (300, 870, 872, 1330) comprises: determining one or more detection metrics, in which the one or more detection metrics are determined by fitting an expected signal shape to one or more sliding sample windows in the scaled data and estimating a parameter fit between the expected signal shape and the scaled data for each window; analyze one or more of the detection metrics; and determining whether signals (300, 870, 872, 1330) exist in the scaled data based on said analyzing one or more of the detection metrics and wherein the step of analyzing the one or more detection metrics comprises: comparing one or more detection metrics detection metrics with a threshold; or modeling one or more detection metrics with a quadratic approximation applied to one or more sliding windows of the detection metric data, and comparing the quadratic coefficients of a plurality of sliding windows of the detection metric. 11. Method, according to claim 8, characterized in that the step of detecting each signal (300, 870, 872, 1330) comprises: determining one or more detection metrics, in which the detection metrics are determined by adjusting - assign an expected signal shape to one or more sliding windows of samples in the scaled data and estimate a parameter fit between the expected signal shape and the scaled data for each window; analyze one or more of the detection metrics; and determining whether there are signals (300, 870, 872, 1330) in the scaled data based on said analysis of one or more detection metrics; and wherein the step of determining the one or more detection metrics is at least partially based on a least squares fit of the expected signal shape to the scaled data, wherein the detection metrics are given by:

where: k is the sample, x (k) represents the detection metric for the K sample, x (k) is a scaled data segment, centered on the K sample, and A is the vector of the centered expected signal shape. 12. Method, according to claim 8, characterized in that the step of detecting each signal (300, 870, 872, 1330) comprises: determining one or more detection metrics, in which the one or more detection metrics are determined by fitting an expected signal shape to one or more sliding sample windows in the scaled data and estimating a parameter fit between the expected signal shape and the scaled data for each window; analyze one or more of the detection metrics; and determining whether there are signals (300, 870, 872, 1330) in the scaled data based on said analysis of one or more detection metrics incrementally updating one or more detection metrics at least partially based on the previous detection metric , using addition, subtraction and/or scaling. 13. Method according to claim 8, characterized in that the step of transforming the output data of the detector further comprises modeling the signal at least partially based on a double exponential waveform, in which the form of double exponential wave is determined by:

where: P(t) is the signal, A is the signal strength, a is the rising edge variable, and b is the falling edge variable. 14. Method, according to claim 8, characterized in that the step of transforming the detector output data is performed by the following operation:

where: x(n) is the received data stream value in sample 'n' a, b determine the rising and falling edges of the signal shape y(n) is the scaled data stream, which may require further scaling. 15. Method according to claim 8, characterized in that: the step of transforming the output data of the detector is at least partially based on the convolution of a finite impulse response filter (FIR) with the output data of the detector.

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