EP1831722A2

EP1831722A2 - Processing a radiation representative signal

Info

Publication number: EP1831722A2
Application number: EP05823783A
Authority: EP
Inventors: Eric Barat; Thomas Dautremer; Jean-Christophe Trama
Original assignee: Commissariat a lEnergie Atomique CEA
Current assignee: Commissariat a lEnergie Atomique et aux Energies Alternatives CEA
Priority date: 2004-12-15
Filing date: 2005-12-14
Publication date: 2007-09-12
Also published as: WO2006064024A2; US20060126763A1; FR2879305B1; WO2006064024A3; US7885775B2; FR2879305A1

Abstract

The invention relates to a method for processing a digital timing noisy signal ykcorresponding to an initial timing signal xt after having been conditioned by a conditioning chain, wherein said initial signal xt represents information on corpuscular radiations transmitted by a radiation source in the form of energy distribution. Said invention is characterised in that it uses a state model representing conditioning applied by said chain in such a way that the initial timing signal xt is converted into the digital timing noisy signal ykin order to obtain the estimation digital non-noisy signal of the initial timing signal xt from the digital noisy signal yk. A system for carrying out said method is also disclosed.

Description

PROCESSING A REPRESENTATIVE SIGNAL OF RADIATION

The field of the present invention relates to the processing of a noisy temporal signal constituting an information carrier making it possible to characterize a set of events produced randomly by an event source.

More particularly, the invention relates in particular to a method for processing a noisy digital time signal yk corresponding to an initial time signal Xt after having been conditioned by a conditioning line, said initial signal Xt being representative of information on radiations. from a source of radiation, these radiations may have an energy distribution.

Such a method, or system capable of implementing such a method, is generally used in the context of detection, counting and measurement of events, such as said emitted radiation.

Its main purpose is the construction of a spectrum for measuring and analyzing the radiation provided by the source.

It will be noted that according to the invention, radiation, any radiation capable of interacting with a detection means so as to have a usable time signal.

In this regard, and by way of non-limiting examples, the radiation targeted by the invention relates in particular to photons, in particular X and gamma, nuclear particles or more generally any particle or any packet of particles. Thus a system of the type of that of the invention may in particular have the object of constructing a spectrum having a number of particles detected at a given energy as a function of energy.

This is particularly interesting in the case of particle sources having an energy distribution.

It is known that a spectrum obtained from such a source may include energy lines that are characteristic of it.

Therefore, from a measurement of the particle source, one can obtain a spectrum which a review by a specialist or software provides access to information on said source of particles.

The examination makes it possible to identify the nature of the source studied.

By way of non-limiting example, in the field of gamma rays, a system of the aforementioned type can provide a spectrum of lines, as shown in FIG. 1, which makes it possible to identify the radioelements that make up this source, and therefore of characterize the latter.

It should be noted, as an indication, that FIG. 1 represents in particular a standard energy spectrum for cesium 137.

In order now to explain a typical operation of the state-of-the-art systems of the aforementioned type, one will rely on an example in the field of gamma spectrometry.

Of course, those skilled in the art can easily extend this example to other categories of radiation including those, for example, stated above.

There is shown by way of example in Figure 2 a signal that could ideally be observed immediately at the output of a gamma photon detector. This signal comprises a plurality of pulses of different amplitude and duration which represent, for example, a current developed in the detector by the passage of a photon.

It will be noted here that they could also represent a voltage in the detector.

In any case, the signal supplied by the detector, the current detector signal, will be referred to later in the text.

To briefly return to the pulses, their width, corresponding to a certain duration in time, is a function of a load collection time.

As mentioned above, the detector current signal shown in FIG. 2 is ideal.

Therefore, such a signal is never observable.

In reality, a preamplifier is generally installed at the output of the detector in order to implement a first shaping of the detector current signal.

Generally two cases of preamplifiers are found in existing systems: capacitive counter-reactive preamplifiers and resistive feedback preamplifiers. As an indication, FIGS. 3 and 4 illustrate a detector 1 followed, respectively, by a capacitive feedback pre-amplifier 2 and a resistive feedback pre-amplifier 3 which comprises a feedback loop between an output and an input. an amplifier 4 composed of a capacitor 5 in parallel with a resistor 6. These preamplifiers are generally followed by a differentiating circuit 7 in the case of a capacitive feedback and a pole-zero PZ 8 correction circuit in the case of a resistive feedback.

The two figures 5 and 6 respectively show an example of an ideal time signal at the output of the two types of preamplifiers mentioned above when they are excited at the input by the same detector current signal, it being understood that noises of an electronic nature are not represented here.

Several stages follow that of pre-amplification, their order and implementation may vary significantly. A known and important step consists in shaping the pulses to extract information of the energy type.

Such a step is often referred to as a "power" shaping step.

By way of non-limiting example, the information can be extracted from a measurement of the amplitude or area of each pulse.

It is assumed that these quantities are generally proportional to an energy.

The choice of the type of shaping "energy" has been the subject of considerable research in recent years in the field of the invention, because this delicate step requires many compromises.

For example, in the case of an extraction of the information from the amplitude of the pulses, a compromise wants that there is an optimum between:

• a very precise obtaining of this information, that is to say a great resolution, The number of pulses per unit of time present in the detector current signal, and

• the fraction of them that we want to keep in the spectrum, for example because of a phenomenon known per se commonly known in the field by the term "stacking" of pulses.

For more details, the reader will be able to refer in particular to the notions of input rate spectrum or OCR (acronym for "Output Count Rate" in English language), and output rate detector or ICR (acronym for "Input Count Rate "in the Anglo-Saxon language).

In order to obtain an optimal solution to this compromise, studies [1], [2] established that the use of a trapezoidal filter could be an optimum solution in the absence of pulse stacks and for a certain kind of noise. Since then, other solutions based on such use have been proposed to improve the performance of the systems.

For example, there are numerous possibilities of producing filters of this type [1-8]: digital, analog or even mixed embodiments, etc. Solutions are also known whose aim is to improve the performances by another means: optimization of said correction PZ [6,9,10,11], optimization of a conventional operation of correcting a baseline [12] , rejection of pulses stacked by correlation between the length and amplitude of a non-stacked pulse [13], etc. But here again, the energy shaping step requires the use of the trapezoidal optimal filter. In summary, the proposed methods and systems include in all cases a trapezoidal filter and more generally an energy shaping step, which is a drawback.

Indeed, although having rendered many services, the performance of systems of this type are nevertheless limited because, in any event, this energy shaping step, and in particular the use of said trapezoidal filter, degrades the current sensor signal-at least the preamplified signal-especially by a time elongation of the pulses.

Consequently, there always comes a time when, as the frequency of occurrence of pulses increases (due to an increase in the frequency of events, for example particle emissions), systems of this type begin to malfunction, producing for example spectra of low resolution or deformed.

This is typically the case at 100,000 to 200,000 counts per second (count rate).

And for the most efficient systems, just 300,000 to 400,000 shots per second can be achieved.

Another disadvantage of the aforementioned systems is that their use is not very flexible. In particular, it is not possible to adapt or modify parameters of the energy shaping step during analysis of the radiation source.

It is therefore necessary in the initial phase to know, at least to estimate as best as possible, the number of pulses per second to adjust the system, and particularly at the level of detection. And, if the number of pulses is overvalued convolution too short will be chosen, which will degrade the resolution.

While, if this number is undervalued too long a convolution will be chosen, which will lead to rejecting many impulses and distorting the spectrum.

By way of non-limiting example, the systems which by their situation can not be adjusted at commissioning only are generally settled on a worst case.

Setting a worst case may include adjusting the system based on the highest measured pulse intensity.

But, this intensity varies over time, so that the system no longer works with optimal adjustment.

An object of the invention is therefore to overcome the aforementioned drawbacks and thus improve the performance of existing systems. In order to achieve this goal, the invention proposes a system and a method that do not implement the energy shaping step systematically used in the state of the art.

For this purpose, the present invention proposes a method for processing a noisy digital time signal yk corresponding to an initial time signal Xt after having been conditioned by a conditioning chain, said initial signal Xt being representative of information on radiations. corpuscular cells originating from a radiation source, said radiations having an energy distribution, characterized in that a state model representative of the conditioning imposed by said chain is used to switch from the initial temporal signal Xt to the time signal noisy digital yk, in order to get from the digital signal noisy yk, a non-noisy digital estimation signal of the initial temporal signal Xt.

Non-limiting preferred aspects of this method are as follows:

the method furthermore comprises a preliminary step in which the noisy digital time signal yk is segmented into successive sections of N samples, so as to obtain a non-noisy digital estimation signal per section;

- the state model includes:

A variable to estimate mk, of the hidden variable type, which can be worth at each sampling step k one of two values to indicate a presence or absence of one or more pulses in the initial temporal signal Xt, to moment corresponding to the step k in question,

A state vector Xk to be estimated, comprising a first component which corresponds to a digitized representation Xk of the initial temporal signal Xt at the instant corresponding to the step k in question,

the hidden variable is a Markovian hidden variable mk which can be equal, at each sampling step k, to the value 1 if the non-noise digital estimation signal must comprise one or more pulses at the sampling step k in question, and 0 if the non-noisy digital estimate signal should have no pulse at said sampling step k;

the method further comprises a step in which an algorithm is implemented which processes the N samples by increasing steps k and cooperates with the state model to provide a filtered estimate Xk / k of the state vector Xk, and therefore to provide a filtered numerical estimation signal Xk / k not noisy that one seeks to obtain, this estimate Xk / k being an estimate conditionally past;

the method further comprises a step in which an algorithm is implemented which processes the N samples by increasing steps k and cooperates with the state model to provide a filtered estimate Xk / k of the state vector Xk, and therefore to provide a noiseless Xk / k filtered numerical estimation signal sought to be obtained, this filtered estimate being a conditionally past filtered estimate from the noisy digital time signal samples yk to step k question; the algorithm is a Kalman filter whose observation corresponds to the noisy digital time signal yk;

the method comprises a step in which the hidden variable mk is estimated at each step k, in order to obtain a signal of occupation representative of an estimate of the presence or absence of one or more pulses at each of the steps k in question, and in that the filter is able to determine, by means of said occupation signal obtained, the filtered estimate Xk / k of the state vector Xk, and thus to determine the filtered numerical estimation signal Xk / k noiseless that one seeks to obtain;

the estimation of the hidden variable mk is implemented by making an assumption that, at the instant corresponding to the sampling step k considered, there is no pulse in the initial time signal Xt, then in verifying if the hypothesis is true by means of a comparison between the square of an innovation I of the Kalman filter and a threshold variable determined by the latter; - Innovation I is of the form:

Ik + l = yk + 1 - yk + l / k where yk + i is the observation at the sampling step k + 1 and yk + i / k a prediction of this observation, at step k + 1, computed from a previously determined prediction Xk + i / k of the vector of state Xk, at step k + 1; - the threshold variable consists of a coefficient multiplied by a variance of innovation I;

the method further comprises a step of implementing a second smoothing algorithm which processes the N samples in decreasing k-steps and which makes it possible to provide an improved smoothed Xk / N estimate of the state vector Xk, and therefore to provide an improved smoothed Xk / N estimate of the signal sought to be obtained, which estimate is conditionally estimated from the past, present and future from the samples of the observation signal yk to the pitch N and the samples of the state vector Xk / ki, previously determined by the first algorithm, from the step k to N; the smoothing algorithm is arranged so that the smoothed estimate Xk / N maximizes in the state vector Xk the probability of having the state vector Xk at the pitch k knowing the N samples of the noisy digital time signal yk , the probability: the method further comprises a step where the energy of the radiations is determined by implementing the following operations:

• find and memorize the step (s) k of each pulse present in the busy signal,

For each of the pulses, read the value of the estimation signal at the stored step (s) corresponding to the pulse considered, and adding the values thus obtained so as to obtain an estimate of the energy of the impulse in question;

the energy of each pulse is weighted according to a measurement of a quality obtained from the estimation signal, this measurement being determined by the Kalman filter or the smoothing algorithm;

the method further comprises a step in which an energy histogram of the radiation source is constructed from the determined energies;

the energy histogram represents a spectrum in energy;

radiation is particle radiation; radiation is radiation from nuclear particles;

radiation is photon radiation;

the method further comprises a radiation detection step which provides the initial time signal Xt;

the conditioning of the initial time signal Xt by the conditioning chain begins with a first step in which the initial signal Xt is pre-amplified and ends in a sampling step at a predetermined frequency fe, so as to obtain the noisy digital time signal yk.

For this purpose, a computer program is also proposed for performing a processing of a noisy digital time signal yk corresponding to a temporal signal Xt, said signal Xt being representative of information on radiation originating from a source of radiation, these radiations having an energy distribution, characterized in that it implements the above-mentioned treatment method according to one or more of the preferred aspects of the above-mentioned treatment method, taken alone or in combination. For this purpose, a system for processing a noisy digital time signal yk corresponding to an initial time signal Xt after having been conditioned by a conditioning chain is proposed, said initial signal Xt being representative of information on radiations. corpuscular particles originating from a radiation source, these radiations having a power distribution, characterized in that it comprises means able to implement a state model, representative of the conditioning imposed by said chain to switch from the initial temporal signal Xt to the noisy digital time signal yk, in order to obtain from the noisy digital signal yk a non-noisy digital estimation signal of the initial time signal Xt.

Preferred non-limiting aspects of this system are the following:

the state model comprises:

A hidden markovian variable to be estimated, which may be equal to the value 1 if the non-noise digital estimation signal must comprise one or more pulses at the sampling step k, and the value 0 if the digital estimation signal is not noisy shall not include any impulses at the sampling interval k,

A state vector Xk to be estimated, comprising a first component that corresponds to a digitized representation Xk of the initial temporal signal Xt at the instant corresponding to the step k in question;

the system further comprises means for implementing a Kalman filter whose observation corresponds to the noisy digital time signal yk, the Kalman filter cooperating with the state model to provide a filtered estimate Xk / k of the vector of Xk state, and therefore to provide a noise-free Xk / k filtered numerical estimation signal that one seeks to obtain, this filtered estimate being a filtered estimate Xk / k conditional on the past from samples of the noisy digital time signal yk to the step k in question;

the system comprises means for implementing a smoothing algorithm;

the smoothing algorithm is arranged so as to maximize in the state vector Xk the probability of having the state vector Xk at the pitch k knowing the N samples of the noisy digital time signal yk; the probability: the conditioning chain comprises a preamplifier and an analog-digital converter;

the preamplifier is of the type chosen from the following list:

- resistive feedback preamplifier,

- capacitive feedback pre-amplifier; the conditioning line also comprises at the output of the preamplifier: a pole-zero correction circuit if the preamplifier is of the resistive feedback type, or a differentiating circuit if the preamplifier is of the capacitive feedback type;

the conditioning line further comprises an amplifier; the packaging line further comprises an anti-aliasing filter;

the conditioning chain is successively constituted, from upstream to downstream, of the preamplifier, of the differentiating circuit if the preamplifier is of the capacitive feedback type, or of the pole-zero correction circuit if the preamplifier is of the counter-type; resistive reaction, amplifier, anti-aliasing filter and analog-to-digital converter; the system comprises storage means for memorizing, in particular, the signals, the state model, the Kalman filter and the smoothing algorithm;

the state model, the Kalman filter and the smoothing algorithm are implemented by a calculation unit 25;

the computing unit is a processor;

the system comprises display means for displaying in particular the results of the estimation.

Thus, according to the invention, it is advantageous to overcome a conventional step of shaping energy that requires various compromises and which in any case leads to degrade the current sensor signal, so the information, especially by time extension impulses it contains.

It is recalled that a consequence of such a compromise is to increase the phenomena of stacks of pulses.

In the invention, the detector current signal is not processed by means of filtering of the type of the prior art; it is estimated, especially using a state model.

This model includes a hidden variable which, once determined, allows first of all a better knowledge of the content, in terms of pulses, of the current detector signal.

A method and a system according to the invention therefore offer many advantages.

In particular, the disadvantage related to the phenomenon of increasing pulse stacks appears for a count rate much higher than in the prior art. Another advantage relates to the flexibility of the invention.

By way of non-limiting example, in the invention, the operation of the method, in particular the algorithms used, is automatically adapted as a function of the counting rate. Thus, no intervention is required once the process initialized, and this both to perform a new parameter setting of an algorithm, for example, that for a radical change thereof given a maladaptation to a rate of counting become too high.

In the invention, the resolution is automatically optimized at the count rate.

Other aspects, objects and advantages of the invention will appear better on reading the following description of the invention, with reference to the appended drawings in which:

FIG. 1, presented in the text above, illustrates an energy spectrum of a cesium 137 source, the axis units being arbitrary,

FIG. 2, shown in an example above, illustrates an ideal detector current signal generated by a gamma ray detector, the axis units being arbitrary, FIG. 3 schematically represents a first example of a part of a known packaging line, comprising downstream of a detector: a capacitive feedback pre-amplifier followed by a differentiating circuit,

FIG. 4 schematically represents a second example of part of a known packaging line, including downstream a detector: a resistive feedback preamplifier followed by a pole-zero correction circuit;

FIG. 5 shows, in a nonlimiting manner, a signal coming from the conditioning chain of the first example, this chain further comprising an analog-digital converter, the units of the axes being arbitrary,

FIG. 6 shows, in a nonlimiting manner, a signal coming from the chain of the second example, this chain further comprising an analog-digital converter, the units of the axes being arbitrary, FIG. 7 schematically shows a complete system enabling implement the method of the invention,

FIG. 8 graphically shows, by way of nonlimiting example, a noise model included in the state model,

FIG. 9 shows, by way of indication and without limitation, a simulation result of an observed time signal yk when the detector current signal is that presented in FIG. 2,

FIG. 10 shows a nonlimiting example of instructions of an embodiment of the Kalman filter,

FIG. 11 represents a busy signal obtained in the case where the observed time signal yk is that of FIG. 9,

FIG. 12 is a temporal graph showing which samples are taken into account at a step k + 1 in the case of the smoothing algorithm and in the case of the Kalman filter,

FIG. 13 shows in a nonlimiting manner steps of the smoothing algorithm, FIG. 14 represents an estimation signal obtained after implementation of the Kalman filter, and then of the smoothing algorithm,

FIG. 15 schematically represents an experimental system capable of implementing the method of the invention and which makes it possible to illustrate the efficiency and the advantages of the invention from measured results.

Referring now to Figure 7, there is shown schematically an embodiment of the system of the invention. Such a system essentially comprises a detector 20 for detecting radiation from a radiation source.

This detector is capable of providing a detector current signal 40 which will be conditioned by a packaging line CH shown in FIG. 7. This packaging line comprises, by way of nonlimiting example, a preamplifier of the aforementioned type, ie the type of resistive feedback or capacitive feedback.

Of course, the invention is not limited to these types of preamplifier. In the conditioning chain CH, the preamplified signal 41 thus obtained is then presented to a block 22 in which a zero-pole correction circuit PZ or a differentiation circuit is used according to the choice made on the type of the preamplifier 21.

The conditioning line CH ends with an analog-digital converter 23 at the output of the block 22. It will be noted here that the packaging line CH as shown in the figure may include many variants that the skilled person will naturally consider.

In particular, the invention is in no way limited to respect such an arrangement of the blocks.

Indeed, it can be envisaged that the analog-digital converter is placed further upstream of the system and that the packaging line CH ends with the block 21 (digital pre-amplification) then 22.

Those skilled in the art will clearly understand that it is simply a matter of making different compromises and of choosing, according to the intended application, a suitable solution.

Note also that according to a variant of the invention the block 22 may implement additional signal conditioning steps. We will see later in a detailed example of an embodiment of the invention that the block 22 may further comprise circuits, such as an amplifier and / or an anti-aliasing filter.

In any case, at the end of the aforementioned CH packaging line, the digitized signal 42 is stored in a dedicated memory 24, then a computing unit 25, such as a microprocessor or a DSP for example

(DSP is the acronym "Digital Signal Processing" in English language), implements calculations from the samples of the memorized signal 43.

It is in particular the unit 25 which implements all the steps making it possible to obtain an estimation signal of the current detector time signal (in the following of the text, this current time signal will be designated detector by Xt) and subsequently an energy histogram of the radiation source studied.

Note that the signals corresponding to the energies of the radiation 44 calculated by the unit 25 are stored in the memory 24 (they can also be stored in a separate memory).

As can also be seen in FIG. 7, this unit 25 manages peripherals 26 such as a display screen, a keyboard, a mouse, etc. We will now describe a preferred embodiment of the method of the invention corresponding to the processing of the digitized signal 42 and implemented in particular by the calculation unit 25.

As a preliminary, it will be noted that k represents a sampling step.

In other words, it designates a sample number and a correspondence with the notion of sampling time can be made using the classical relation: t = k / fe, where t is the sampling time and fe the sampling frequency of the converter 23.

It will also be noted that a variable index k / k will designate an estimate obtained from the first algorithm, in particular from the Kalman filter; an index k / N denotes an estimate obtained from the second algorithm, in particular from the smoothing algorithm; an index k + l / k will designate a prediction of the indexed variable as such.

Finally, Xk will designate a digital representation that we want to estimate of the Xt signal. According to a preferred embodiment of the method of the invention, the computing unit 25 proceeds first of all with a segmentation of the signal 42 which has been previously stored in the memory 24.

Such a segmentation is arranged so as to obtain successive sections of N samples.

Now, as will be seen, the computing unit 25 will then deduce the noisy digital time signal yk from the signal 42.

Thus, by implementing the method of the invention, an estimation signal in constituted sections will be obtained. In this regard, in order to return to the best possible estimate of the signal Xt from the signal yk, the calculation unit 25 implements a state model representative of the conditioning imposed by said chain CH to switch from the signal Xt to yk signal.

We recall here that a model of state is model which can always be defined in the following way:

or :

- k is a discrete time; - Xk, Uk, Yk are respectively state, control and observation vectors of respective dimensions n, m, r;

- (Wk) k and (Vk) k are two independent Gaussian white noise of respective covariance matrices Qk and Rk;

the initial state Xo is Gaussian of average mo, of covariance Po and is independent of the sequences (Wk) k and (Vk) k, Fk is a state transition matrix, Hk is an observation matrix, Gk and Jk are respectively state and observation control matrices, Bk and Dk are noise matrices respectively of state and of observation. 'observation.

The reader will also be able to refer to reference works known in the field to obtain definitions of a state model [15-

17].

The state model of the invention includes a hidden variable, denoted im, that is to say a variable to be determined, but which can not be equal to two distinct values to choose from. One of the values corresponds to an indication that at the sampling instant corresponding to the step k considered, the signal Xt comprises one or more pulses, while the other value corresponds to an indication that at said instant of sampling , the signal Xt does not include a pulse. In particular, if there is at least one pulse at a step k, the value is 1 and in the absence of a pulse the value is 0.

Thus, from this hidden variable mk, there is a binary signal which provides a first information on the signal Xt, namely a state of occupation of this signal. This binary signal, signal of occupation, will be called later.

According to a preferred embodiment of the invention, the hidden variable is a Markovian variable so that the state model becomes of the HMM (Hidden Markov Model) type.

An example of this state model is shown below. We note in the following equations dk the digitized signal 42 from the converter 23. On the other hand, the noisy digital time signal yk will also be called the observation signal yk.

A transfer function of the preamplifier 21 and the element 22 constituting a differentiating circuit or P / Z is written:

T (z) = 1 - β

1 - β z ^"1 with β = e- ^2πf ' ^{τ *} where Te is the sampling period, f _{P is} the frequency of the residual pole after P / Z or differentiation.

_ _d ^ β_

^{Yk ~} l -β 1 -β ^{k "x}

The conditioning chain CH can now be described by the following state system.

| X _k = FX _k _ _{1 +} D (m _k ) .W _k 1 Y _k = HX _k with,

or,

Xk is a state vector that one seeks to estimate, this vector comprising as first component said numerical representation Xk that one seeks to estimate the signal Xt. mk is the Markovian hidden variable or in other words the said occupation signal, it will be further noted that no priori is given on the form of the signal Xt except for its positivity,

- bk is a bias corresponding to a baseline of the form: ηk being a Gaussian random variable of zero mean and standard deviation Ob,

- Wk an observation noise related to yk of the form: w _k = ε _k - α ε _k _ ₁₇ εk being a Gaussian random variable of zero mean and standard deviation On, α being a time constant characteristic of observation noise Wk, related to a characteristic frequency fc of this noise having the following form: α = e ^{~ 2πf} ° ^Te ,

it will be noted that in this example of a state model, the noise model adopted is identical to that considered in conventional approaches, for example in publications [1] and [2]; in this respect, FIG. 8 schematically represents this noise model in terms of power depending on the frequency,

- Vk is an internal state noise related to 8k by a relation of the form:

Wk is a noise vector of the form: w. k = η _k ε _k where μk is a dynamic noise, ie a Gaussian variable of zero mean and standard deviation σ _P ,

F is a matrix of passage of the form: 0 0 0 0

0 1 0 0

F =

0 0 0 1

0 0 0 0

H is an observation matrix of the form:

H = [1 1 1 0], D (nik) is a so-called jump matrix of the form: m _k 0 0

0 1 0

D {m _k ) =

0 0 1

0 0

Finally, we define:

N the length of a section or the last index k possible in the section, Q and H 'of the matrices of the following form: σ; 0 0

Q = 0 σ; 0

0 0 σ _n ²

and, H '= [0 1 1 O].

Thus, from the equations above, we can see that a knowledge of the state vector Xk automatically leads to the knowledge of Xk.

Therefore in the following text we can consider that the estimation of a component of a vector (xk for example) will in any case be deduced from an estimate of the vector comprising this component (Xk according to the above example) . Taking into account the equations above, the observation signal yk can be expressed in the following way: yk = ^χ k ^{+ b} k ^{+ w} k

In order to illustrate the possible form of such a signal, FIG. 9 shows as a nonlimiting indication a simulation result of the observed time signal yk when the ideal detector current signal corresponds to that presented in FIG.

Since the state model is thus established, it is provided in a preferred embodiment of the invention to implement an algorithm that processes the N samples of a section by increasing steps k and that cooperates with the state model to provide a first filtered estimate Xk / k of the state vector Xk, thereby determining the busy signal.

As mentioned above, the filtered estimate Xk / k inevitably provides a filtered estimate Xk / k of Xk. It will be noted that such an estimate represents an estimate conditionally in the past, which means for a statistician that it has been implemented at essentially from the samples of the observation yk to the step k in question.

In the embodiment presented here, the algorithm is a Kalman filter and the observation of this filter is the observation signal yk.

As we will see below we proceed to the estimation of Xk using this filter in two steps.

The first step is to determine all the mk, thus the entire occupancy signal, and the second step uses the busy signal to update the state model parameters and thus obtain the filtered estimate Xk / k . In the first step, the determination of the busy signal mk is implemented by making the assumption that, at the instant corresponding to the sampling step k, there is no pulse in the initial temporal signal. xt. The variable mk is therefore initially equal to 0 regardless of the value of the step k.

We then verify if this hypothesis is true by comparing the square of an innovation I of the Kalman filter and a threshold variable predetermined by the latter. According to the invention, the innovation reflects the difference between the observation yk and the prediction that is made from a prediction Xk + i / k of Xk.

More precisely, innovation I at a step k + 1 can be expressed as follows: where yk + i is the observation at the sampling step k + 1 and yk + i / k the prediction of this observation at step k + 1 given the first k samples, this one being computed from the prediction Xk + i / k previously determined from the state vector Xk, at step k + 1 given the first k samples.

If, at a step k, the innovation has a value greater than said threshold, it is considered that said hypothesis is not verified, that is to say that at the step in question the variable must be equal to 1 so that the signal occupation contains an impulse.

In a preferred embodiment of the invention, the threshold value allowing the comparison with the innovation is a multiple of the variance of the innovation I. In this respect there is shown in Figure 10 a non-limiting example of instructions corresponding to this first step.

The first step is to implement an initialization of the parameters.

Instructions in this step are given by way of nonlimiting example below. It will be noted as a preliminary that the symbol * associated with a matrix denotes the conjugate matrix.

k = 0

mo = O β is between 3 and 5

where Pk / k is a matrix corresponding to the variance of the filter estimation error of Xk.

It can be seen now in FIG. 10 that the steps that follow this initialization step INIT are integrated in an incremental loop 106, 106 'on step k, starting with k equal to 0 and ending in k equal to N-I.

In this regard, attention is drawn to the fact that in this loop are integrated this first step of the Kalman filtering but also the second step described below. Of course, the invention also provides that it is possible to implement each of these two steps independently by using a first loop in the first step and a second loop in the second step. In all cases, the first step begins with an initialization at step k = 0, in particular of the state vector Xo / o, the hidden Markov variable mo, the parameter β (preferably of the order of 3 to 5), and the matrix Po / o corresponding to the variance of the estimation error of the state vector Xk.

Referring again to FIG. 10, the step following the initialization step is step 100.

In this step 100, the prediction Xk + i / k is determined from, in particular, the estimate Xk / k.

In the next step 101, the innovation Ik + i is determined, and the variance of the innovation under the hypothesis mk = 0 is determined in step 102. Step 103 corresponds to the test to determine if the assumption of no pulse at the k + 1 step in question is true.

As can be seen in this step, the variance is multiplied by the square of the coefficient β, the result being compared to the square of the innovation I.

If the gap between the innovation and the variance multiple is greater than or equal to zero, the filter then assumes that the assumption is false.

The busy signal must then indicate the presence of a pulse, the hidden variable at step k + 1 takes the value 1.

If necessary, the busy signal to indicate the absence of a pulse, the hidden variable retains the value 0 at step k + 1. As an indication, FIG. 11 shows the occupancy signal obtained in the case where the observation signal yk is that of FIG. 9. As can be seen, this signal comprises vertical sticks of value 1 more or less spaced in time and of greater or lesser duration.

A comparison with FIG. 2 shows that the first step of estimating the occupancy signal, and thus the hidden variable, works well.

As mentioned above, in the second step the occupancy signal is used to update the parameters of the state model and thus obtain the filtered estimation signal Xk / k by the filtered estimate Xk / k of the vector of state Xk.

Instructions 107 to 109 of this second step are given by way of non-limiting example still in FIG. 10, following steps 104 or 105 according to the result of the test 103.

And as we can see, this second step makes it possible to go from the forecast Xk + i / k used in the first step, to the estimate

Xk + i / k + i at step k + 1 (step 108).

Step 110 marks the end of the implementation of the Kalman filter thus defined.

Thus, at this step 110, an estimation signal Xk / k of the signal Xt, in this case the current detector signal, is available, this signal having less noise than the observation yk, and this without having resorted to a energy shaping step of the prior art.

In another embodiment of the invention, the quality of the estimation signal is further improved by implementing a second smoothing algorithm which processes the N samples in decreasing k-steps and which makes it possible to provide an Xk / N smoothed estimate. improved state vector Xk. Therefore, this algorithm provides a smoothed estimate signal Xk / N that is sought to obtain.

On the other hand, it should be noted that such a smoothed estimate Xk / N is an estimate conditional on past, present and future. This expression means for a statistician that the estimation is carried out essentially from the samples of the observation signal yk to pitch N and the samples of the state vector Xk / ki, previously determined by the first algorithm, and it's from k to N.

And in a preferred variant of this embodiment, this smoothing algorithm is arranged so as to maximize Xk the probability of having the state vector Xk at the step k knowing the N samples of the observation signal yk, ie the probability :

FIG. 12 shows a temporal graph showing which samples are taken into account in the case of smoothing (axis 151) and in the case of the Kalman filter (axis 150), knowing that in this figure these two algorithms are supposed to implement k + 1 step calculations. Moreover, steps of this smoothing algorithm are given in FIG.

Briefly, we start here again with an initialization, denoted INIT2.

Then, we perform a decremental loop on k in which we perform the following calculations: F _k = FF.K _k .H

^Λ k / N ~ ^r k ^lΛ; k + l / N ^" • ^" "- ^V k - ^fc k

^/ ^AV k / N - - F ^r k ^* - ^/ Λ ^V k + l / N - F ^r k + ⁺ F ^tl T -v ^V k ^{1 •} H "- ^ ^• k / N ⁼ " ^ -k / kl ⁺ "k / k-1 - ^ k / N

P * k / N - P ¹ Wk-I - P ^ι k / kl - ⁱ Λ ^v k / N - P ¹ k / k-1

FIG. 14 shows the final non-noise numerical estimation signal Xk / N resulting from the implementation of the aforementioned method.

It can be seen that the non-noisy digital estimation signal Xk / N has pulses that correspond well to those of FIG. 9, and that the noise has disappeared.

An object of the invention is to provide an energy spectrum of the radiation source studied, the method may further comprise additional steps for generating an energy signal from the estimation signal Xk / k or Xk / N, depending on whether Kalman filtering is implemented only or that it is supplemented by the smoothing algorithm.

For this purpose, we first start by analyzing the busy signal to identify the instants of presence of pulses.

The steps k corresponding to these instants are stored in the memory 24.

The estimation signal, for example Xk / N, is then used to search and store its values at the stored steps k.

Finally, assuming that the energy of the pulses is proportional to its amplitude or its area, one adds for each of them the stored values associated with the corresponding steps k.

For example if a ninth pulse in the busy signal lasts three steps k = 10, 11, 12 and for these three steps k the estimation signal The non-noisy digital has the respective values lkeV, l.lkeV and 1.05keV, the determination of the energy of the ninth pulse will result in the result 3.15keV.

By proceeding in this way on all the pulses identified in the busy signal, the method is then able to provide a histogram of the energies thus estimated.

According to one variant, the preceding estimate of the energies can also be refined by weighting them by a coefficient which represents, for example, a measurement of an estimate quality finally obtained. It will be noted in this respect that the smoothing algorithm advantageously provides the variance of the smoothing estimation error Pk / N.

We can then weight the previous estimate of energies by means of Pk / N.

It will also be noted that the Kalman filter also provides the variance of the filter estimation error, denoted Pk / k.

However, the latter is less precise than that provided by the smoothing algorithm.

In all cases, the applicant considers that the use of such weighting can generate a higher quality energy histogram.

As an indication now, it will be noted that the method of the invention initially comprises steps which make it possible in particular to estimate at best the baseline level of the signal (or bias) in order to start, for example, the Kalman filtering in the best possible way. conditions. This is done using a robust method of taking the histogram mode of the values taken by the first samples of the observation signal yk.

As regards the noise parameters α, σ _n , σt>, they can be estimated by spectral analysis of the detector current signal, and for example in areas where few pulses are present.

As for σ _P, it is generally fixed at a value much greater than σ _n and

Ob.

In order to illustrate the efficiency and advantages of the method of the invention, we will now present a detailed embodiment of an experimental system designed by the applicant as well as measurement results obtained from it.

Of course, the invention does not intend to be limited to this embodiment and the skilled person will understand that there are naturally many possible variants of such a system design.

Referring to FIG. 15, there are essentially blocks 20 to 25 shown in FIG. 7, that is to say from upstream to downstream:

a detector 20,

a conditioning chain comprising a preamplifier 21, a block 22 in which a pole-zero correction circuit is used

PZ or a differentiation circuit according to the choice focused on the type of preamplifier 21, and an A / D converter 23,

a memory 24 for the storage of the signals and a memory 27 for the storage of the energies controlled by a calculation unit 25. Nevertheless, a difference with the system of FIG. 7 is that the conditioning line CH furthermore comprises an amplifier 22 'and an anti-aliasing filter 22 "arranged between the block 22 and the A / D converter 23.

Discussion on a design of blocks 21 to 22 "

It is first of all necessary to limit a saturation of the amplifier 22 ', in particular because of a counting rate that is too high.

For this purpose, it is proposed to filter the output signal of the preamplifier 21 with the aid of block 22 (Pole / Zero for the resistive preamplifier, high-pass for resetting) so that the time constant of the pole residual in the present case of the order of 500 ns.

Indeed, such a value allows operation at input rates of several million shots per second.

Of course, the use of today more advanced technologies and advanced technologies in themselves would reduce this time constant and further increase the performance of the system.

Analog / digital converter 23

It is proposed to construct here significant histograms of 2 ¹⁴ channels. Given the technology used, a converter with a resolution of 14 bits was selected.

Currently, the sampling frequency fe is limited by the performance of the converters and by the capabilities of the computing unit to perform the processing of the digitized data stream in real time. The bandwidth of the signals from the detector 20 may exceed 30 Mhz, which would lead to a prohibitive sampling rate for the current technology.

This is why it is proposed to insert in the conditioning chain, upstream of the conversion, a spectrum anti-aliasing filter 22 "which ensures a sufficient attenuation of frequencies greater than half the sampling frequency.

An allowable sampling frequency is between 10 and 20MHz, currently.

Digital Processing Unit: Blocks 24 to 27

This unit must be sized to perform the calculations related to the presented algorithms.

It can be for example a processor of the consumer market. The samples are conveyed from the converter 23 to the memory 24 of the section calculation unit.

In order to process all the samples, the invention proposes, by way of nonlimiting example, a "ping-pong" operation: a sample section is stored in memory while the computing unit processes a range located in another portion of his memory.

At the end of an implementation of the Kalman filter and the smoothing algorithm, the pulses are identified by analyzing the busy signal as described above and the corresponding energies are stored in the memory 27. In this respect, the signal memories 24 and 27 are not necessarily distinct from the calculation unit 25. In this case, in the system presented here these memories are integral parts of the memory of this unit 25.

The following values have been measured with a prototype system whose implementation is described in the previous paragraph. In particular, on this system the available computing power does not allow to go beyond a sampling of 10 MHz on 14 bits.

Despite this, it was possible to achieve a count rate of 5 million counts per second with a standard coaxial germanium detector of 20% efficiency. At all count rates, the spectra provided are compatible with commercially available gamma spectrum processing software, especially peak forms are well Gaussian.

The resolution typically achieved at low count rate is 1.7 keV @ 1332 keV, a little better than the manufacturer resolution announced at 1.8 keV, due in particular to a very neat analog electronics.

The resolution decreases with the increase of the counting rate, but nevertheless, for example, about 2 keV @ 1332 keV per 100,000 shots per second (ICR) is reached, and about 3 keV @ 1332 keV at 1 million shots per second. second (ICR), these examples being given considering an increasing disturbing source of Cesium 137 and a stable reference of Cobalt 60.

As mentioned above, the method of the invention adapts automatically and in real time to the counting rate.

Consequently, during this experiment, an initial setting was implemented, but no other such intervention took place once the process was started, despite a change in the count rate during execution of the process. Of course, many modifications can be made without departing from the scope of the present invention.

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Claims

1. A method for processing a noisy digital time signal yk corresponding to an initial time signal Xt after having been conditioned by a conditioning line, said initial signal Xt being representative of information on corpuscular radiation (30) originating from a radiation source, these radiations (30) having an energy distribution, characterized in that a state model representative of the conditioning imposed by said chain is used to switch from the initial time signal Xt to the noisy digital time signal. yk, in order to obtain from the noisy digital signal yk, a non-noisy digital estimation signal of the initial time signal Xt.

2. Processing method according to claim 1, characterized in that it further comprises a preliminary step where the noisy digital time signal yk is segmented into successive sections of N samples, so as to obtain a digital estimation signal. not noisy by section.

3. Treatment method according to one of the preceding claims, characterized in that the state model comprises:

a variable to estimate mk, of the hidden variable type, which may be worth at each sampling step k one of two values to indicate a presence or absence of one or more pulses in the initial temporal signal Xt, to moment corresponding to the step k in question, a state vector Xk to be estimated, comprising a first component which corresponds to a digitized representation Xk of the initial temporal signal Xt at the instant corresponding to the step k in question,

4. Processing method according to claim 3, characterized in that the hidden variable mk is a Markovian hidden variable that can be equal, at each sampling step k, to the value 1 if the non-noise digital estimation signal must comprise one or more pulses at the sampling step k in question, and at the value 0 if the non-noise digital estimation signal must have no pulse at said sampling step k.

5. Processing method according to one of claims 3 to 4, characterized in that it further comprises a step where it implements an algorithm that treats the N samples by increasing k steps and which cooperates with the model to provide a filtered estimate Xk / k of the state vector Xk, and thus to provide a filtered, non-noisy Xk / k filtered estimation signal which is sought to be obtained, this filtered estimation signal Xk / k k corresponding to an estimate filtered conditionally in the past.

6. Processing method according to the preceding claim, characterized in that it further comprises a step where it implements an algorithm that processes the N samples by increasing k steps and cooperates with the state model to provide a filtered estimate Xk / k of the state vector Xk, and therefore to provide a filtered noise-free estimate Xk / k that is sought to obtain, this filtered estimation signal Xk / k corresponding to an estimate conditionally filtered from the samples of the noisy digital time signal yk to the step k in question.

7. Processing method according to one of claims 5 to 6, characterized in that the algorithm is a Kalman filter whose observation corresponds to the noisy digital time signal yk.

8. Processing method according to one of claims 3 to 7, characterized in that it comprises a step wherein the hidden variable mk is estimated at each step k, in order to obtain a representative occupation signal of an estimate of the presence or absence of one or more pulses at each step k in question, and in that the filter is able to determine, by means of said occupation signal obtained, the filtered estimate Xk / k of the vector of state Xk, and thus to determine the filtered numerical estimation signal Xk / k non-noisy that is sought to obtain.

9. Treatment method according to the preceding claim, characterized in that the estimate of the hidden variable mk is implemented by making an assumption that, at the instant corresponding to the sampling step k considered, there exists no impulse in the initial temporal signal Xt, then checking whether the hypothesis is true by means of a comparison between the square of an innovation I of the Kalman filter and a threshold variable determined by the latter.

10. Treatment method according to the preceding claim, characterized in that the innovation I is of the form: where yk + i is the observation at the sampling step k + 1 and yk + i / k a prediction of this observation, at step k + 1, computed from a previously determined prediction Xk + i / k of the vector of state Xk, at step k + 1.

11. Processing method according to one of claims 9 to 10, characterized in that the threshold variable consists of a coefficient multiplied by a variance of the innovation I.

12. Processing method according to one of claims 3 to 11, characterized in that it further comprises a step where it implements a second algorithm, said smoothing algorithm, which processes the N samples in steps k decreasing and which provides an improved smoothed Xk / N estimate of the state vector Xk, and thus provides an improved smoothed Xk / N estimate of the signal sought to be obtained, which estimate is conditionally predicted, in the present and in the future from the samples of the observation signal yk to the pitch N and the samples of the state vector Xk / ki, previously determined by the first algorithm, from the pitch k to N.

13. Processing method according to the preceding claim, characterized in that the smoothing algorithm is arranged so that the smoothed estimate Xk / N maximizes in the state vector Xk the probability of having the state vector Xk in the step k knowing the N samples of the noisy digital time signal yk, the probability:

14. The method of treatment according to one of the preceding claims, characterized in that it further comprises a step wherein the energy of the radiation is determined by implementing the following operations:

• find and memorize the step (s) k of each pulse present in the busy signal,

For each of the pulses, read the value of the estimation signal at the memorized step (s) corresponding to the pulse considered, and add the values thus obtained so as to obtain an estimate of the energy of the impulse in question.

15. Treatment method according to one of the preceding claims 12 to 14, characterized in that the energy of each pulse is weighted according to a measurement of a quality obtained from the estimation signal, this measurement being determined by the Kalman filter or the smoothing algorithm.

16. The method of treatment according to one of the preceding claims, characterized in that it further comprises a step of constructing an energy histogram of the radiation source from the determined energies.

17. Process according to the preceding claim, characterized in that the energy histogram represents an energy spectrum.

18. Processing method according to one of the preceding claims, characterized in that the radiation is particle radiation.

19. Treatment method according to one of the preceding claims, characterized in that the radiation is nuclear particle radiation.

20. Treatment process according to one of claims 1 to 18, characterized in that the radiation is photon radiation.

21. The method of treatment according to one of the preceding claims, characterized in that it further comprises a radiation detection step which provides the initial time signal Xt.

22. Processing method according to one of the preceding claims, characterized in that the conditioning of the initial time signal Xt by the conditioning chain begins with a first step where the initial signal Xt is preamplified and results in a step of sampling at a predetermined frequency, so as to obtain the noisy digital time signal yk.

23. A computer program for performing a processing of a noisy digital time signal yk corresponding to a time signal Xt, said signal Xt being representative of information on radiation from a radiation source, said radiation having a distribution of energy, characterized in that it implements the treatment method according to any one of claims 1 to 23.

24. A system for processing a noisy digital time signal yk corresponding to an initial time signal Xt after having been conditioned by a conditioning line, said initial signal Xt being representative of information on corpuscular radiation coming from a source of radiation, these radiations having a distribution in energy, characterized in that it comprises means able to implement a state model, representative of the conditioning imposed by said chain to go from the initial time signal Xt to the noisy digital time signal yk, in order to obtain from the noisy digital signal yk a non-noisy digital estimation signal of the initial time signal Xt.

25. Processing system according to claim 24, characterized in that the state model comprises:

a hidden markovian variable to be estimated, which may be equal to the value 1 if the non-noise digital estimation signal must comprise one or more pulses at the sampling step k, and the value 0 if the digital estimation signal is not noisy shall not include any impulses at the sampling interval k, a state vector Xk to be estimated, comprising a first component that corresponds to a digitized representation Xk of the initial temporal signal Xt at the instant corresponding to the step k in question.

26. Treatment system according to one of claims 24 to 25, characterized in that it further comprises means for implementing a Kalman filter whose observation corresponds to the noisy digital time signal yk, the cooperating Kalman filter. with the state model to provide a filtered estimate Xk / k of the state vector Xk, and thus to provide a noiseless Xk / k filtered numerical estimation signal which is sought to be obtained, this filtered estimate being a filtered estimate Xk / k conditional on the past from samples of the noisy digital time signal yk to the step k in question.

27. Treatment system according to one of claims 24 to 26, characterized in that it comprises means for implementing a smoothing algorithm.

28. Treatment system according to claim 27, characterized in that the smoothing algorithm is arranged so as to maximize in the state vector Xk the probability of having the state vector Xk at the pitch k knowing the N samples the noisy digital time signal yk; the probability: p (Xk / yi to VN)

29. Treatment system according to one of claims 24 to 28, characterized in that the conditioning chain comprises a preamplifier (21) and an analog-digital converter (23).

30. Treatment system according to claim 29, characterized in that the preamplifier (21) is of the type chosen from the following list:

- resistive feedback preamplifier,

- capacitive feedback pre-amplifier.

31. Treatment system according to one of claims 24 to 30, characterized in that the conditioning chain further comprises at the output of the preamplifier (21): a pole-zero correction circuit (22) if the preamplifier is of the type resistive feedback, or a differentiating circuit (22) if the preamplifier is of the capacitive feedback type.

32. Treatment system according to claim 24 to 31, characterized in that the conditioning chain further comprises an amplifier (22 ').

33. Treatment system according to claim 24 to 32, characterized in that the packaging line further comprises an anti-aliasing filter (22 ").

34. Treatment system according to claim 33, characterized in that the conditioning chain is successively constituted, from upstream to downstream, of the preamplifier (21), of the differentiating circuit (22) if the preamplifier is of the capacitive feedback type, or the pole-zero correction circuit (22) if the preamplifier is of the resistive feedback type, the amplifier (22 '), the anti-aliasing filter (22 ") ) and the analog-to-digital converter (23).

35. Treatment system according to one of claims 24 to 34, characterized in that it comprises storage means (24,27) for storing, in particular, the signals, the state model, the Kalman filter and the smoothing algorithm.

36. Processing system according to one of claims 27 to 35, characterized in that the state model, the Kalman filter and the smoothing algorithm are implemented by a computing unit (25).

37. Treatment system according to claim 36, characterized in that the computing unit (25) is a processor.

38. Processing system according to one of claims 24 to 37, characterized in that it comprises means (26) for displaying in particular the results of the estimation and data entry.