JP6386997B2 - X-ray computed tomography apparatus and correction method - Google Patents

Description

  Embodiments described herein relate generally to an X-ray computed tomography apparatus and a correction method.

  In the simplest expression, radiation imaging relates to the total attenuation per ray of the X-ray beam that traverses the subject and the detector. Attenuation results from the same comparison of rays with and without the subject present. From this conceptual definition, several steps are required to properly construct an image. For example, “limited size of the X-ray generator”, “characteristics and shape of the filter that blocks very low energy X-rays from the X-ray generator”, “geometry and characteristics of the detector” “Detailed information” and “capacity of the data acquisition system” are all factors that influence how the actual reconstruction is performed. In image reconstruction, a linear attenuation coefficient (LAC: Linear Attenuation Coefficient) map of a subject to be imaged is obtained from LAC line integration by inverse Radon transform. Line integral is related to the logarithm of the intensity of the main X-rays passing through the subject. However, the X-ray intensity measured at the detector can include scattered photons and primary photons. Thus, an image reconstructed from intensities with mixed scattered X-rays may contain some scattering artifacts.

  A third generation CT system can include sparsely distributed fourth generation photon counting detectors. In such a combination system, the fourth generation detector collects the primary beam through the range of detector fan angles.

  Many clinical applications can benefit from spectral CT technology. For example, spectral CT technology can provide material differentiation and improved beam hardening correction. Furthermore, semiconductor-based photon counting detectors are promising candidates for spectral CT. For example, the detector can provide better spectral information compared to conventional spectral CT techniques (eg, dual light source, kVp-switching, etc.).

JP2013-192951A

  The problem to be solved by the present invention is to provide an X-ray computed tomography apparatus and a correction method capable of improving the accuracy of pile-up correction.

The X-ray computed tomography apparatus according to the embodiment includes an X-ray tube, an X-ray detector, a generation unit, a generation control unit, and a reconstruction unit. The X-ray tube generates X-rays. The X-ray detector detects X-ray photons generated from the X-ray tube and outputs a measurement spectrum. The generation unit generates a composite spectrum based on a parameter vector including a parameter related to a probability of a pile-up event and a parameter related to the dead time of the X-ray detector. The generation control unit includes a parameter related to the probability of the pile-up event so that the degree of difference between the measured spectrum output by the X-ray detector and the synthesized spectrum generated by the generation unit is below a predetermined threshold. The generation unit is controlled to generate the synthesized spectrum while changing the parameter vector. The reconstruction unit generates a correction spectrum in which the pile-up event is corrected based on a combined spectrum in which the degree of difference falls below a predetermined threshold, and reconstructs an image based on the generated correction spectrum.

FIG. 1 is a diagram illustrating an example of the configuration of the X-ray CT apparatus according to the present embodiment. FIG. 2 is a flowchart showing a procedure of processing by the detector pileup model according to the present embodiment. FIG. 3 is a flowchart showing a processing procedure by the model parameter estimation device according to the present embodiment. FIG. 4 is a diagram showing the sum of component spectra obtained by the detector pileup model according to the present embodiment. FIG. 5 is a diagram showing the sum of component spectra calculated with a constant detection probability. FIG. 6 is a diagram showing an X-ray CT apparatus according to the present embodiment. FIG. 7 is a diagram showing the CT scanner system according to the present embodiment.

  Hereinafter, embodiments of an X-ray computed tomography apparatus and a correction method will be described in detail with reference to the accompanying drawings. The embodiments described herein, and many of the attendant advantages, will be better understood and more fully understood by reference to the following detailed description when considered in conjunction with the accompanying drawings. Is easy. Hereinafter, the X-ray computed tomography apparatus is referred to as an X-ray CT apparatus.

  Embodiments of the present application generally relate to pile-up correction for a photon-counting detector of a spectral computed tomography (CT) system, specifically the embodiments described herein. Is directed to a new X-ray CT apparatus for pile-up modeling and correction for a fourth generation spectral photon counting CT detector.

  According to one embodiment, the X-ray CT apparatus includes an X-ray tube, an X-ray detector, a generation unit, a generation control unit, and a reconstruction unit. The X-ray tube generates X-rays. The X-ray detector detects X-ray photons generated from the X-ray tube and outputs a measurement spectrum. The generation unit generates a composite spectrum based on a parameter vector including a parameter regarding the probability of a pile-up event and a parameter regarding the dead time of the X-ray detector. The generation control unit generates the synthetic spectrum while changing the parameter vector so that the degree of difference between the measurement spectrum output by the X-ray detector and the synthetic spectrum generated by the generation unit falls below a predetermined threshold. Control the generator. The reconstruction unit generates a correction spectrum in which the pile-up event is corrected based on the combined spectrum whose difference is below a predetermined threshold, and reconstructs an image based on the generated correction spectrum.

  According to one embodiment, according to one embodiment, the X-ray CT apparatus includes an X-ray tube, an X-ray detector, a generation unit, a generation control unit, and a reconstruction unit. The X-ray detector detects X-ray photons generated from the X-ray tube and outputs a measurement spectrum. The generation unit includes a parameter related to a probability of a single photon incident event, a probability of an incident event of two photons, and a probability of a pileup event including a probability of an incident event of at least three photons and a parameter related to a dead time of the X-ray detector A composite spectrum is generated based on the included parameter vector. The generation control unit controls the generation unit to generate a synthetic spectrum in which the degree of difference between the measurement spectrum output by the X-ray detector and the synthetic spectrum generated by the generation unit is below a predetermined threshold. The reconstruction unit generates a correction spectrum in which the pile-up event is corrected based on the combined spectrum whose difference is below a predetermined threshold, and reconstructs an image based on the generated correction spectrum.

  The above-described embodiments are realized, for example, by a method for determining a parameter vector including a plurality of parameters of a detector pileup model of a photon counting detector. Here, the detector pile-up model is used for pile-up correction for a spectrum computed tomography scanner (X-ray CT apparatus). For example, the above-described method includes (1) dead time, simple A setting step for setting values of a plurality of parameters including a probability of a one-photon incident event, a probability of a two-photon incident event, and an individual probability of different pileup events including a probability of at least a three-photon incident event; A plurality of component spectra, each corresponding to one of the individual probabilities of different pile-up events, using (a) a detector response model, (b) an incident spectrum, and (c) a parameter vector setting. And (3) summing a plurality of component spectra to obtain an output spectrum (synthesis (4) a calculation step for calculating a cost function value based on the output spectrum and the measured measurement spectrum, and (5) at least one of the parameter vector values. And (6) an iterative step that repeats the steps of determining, summing, calculating, and updating until a stop criterion is met so that a parameter vector that optimizes the cost function can be determined. Is included.

  In one embodiment, the setting step includes setting a dead time parameter based on the scanner shape (characteristic for each detection element of the X-ray detector).

  In another embodiment, the calculating step includes the step of calculating the value of the cost function using the following equation (1).

Here, Ψ (a) is a cost function, a is a parameter vector, S _out (E, a) is an output spectrum (combined spectrum), S _M (E) is a measured spectrum, and E is energy.

  In another embodiment, the parameter further includes a time threshold that distinguishes between a peak pileup event and a tail pileup event, and the determining step includes the peak pileup component spectrum and the tail pileup component of the two-photon incident event. Determining a spectrum.

  In another embodiment, the iterative step includes iterating the determination, summing, calculating, and updating steps until the cost function falls below a predetermined threshold or within a predetermined number of iterations.

  In another embodiment, the updating step includes updating the parameter vector a by an exhaustive search method.

  In another embodiment, the updating step includes updating the parameter vector a by a non-linear least square method.

  In another embodiment, the determining step includes determining a first component spectrum corresponding to the single photon incident event as one of the plurality of component spectra, wherein the first component spectrum is: It is determined as in (2).

Here, S _in is an incident spectrum, n is an incident count rate, μ _CZT (E) is a linear attenuation value, z is a depth, and τ _d is a dead time.

  In another embodiment, a method for performing pile-up correction for a spectral computed tomography scanner (X-ray CT apparatus) is provided. Here, the X-ray CT apparatus includes a photon counting detector, and the method includes (1) a parameter vector including a plurality of parameters of a detector pileup model of the photon counting detector using the above-described method. Using (2) performing a scan using a scanner and generating a measured spectrum for the photon counting detector; and (3) using a detector pileup model and the measured spectrum. Determining an incident spectrum for the photon counting detector.

  In another embodiment, a device is provided for determining a parameter vector comprising a plurality of parameters of a detector pileup model of a photon counting detector. Here, the detector pile-up model is used for pile-up correction for an X-ray CT apparatus, and the device includes, for example, (1) dead time and single photon incident event probability, Setting values of a plurality of parameters including a probability of a two-photon incident event and an individual probability of different pileup events including a probability of at least a three-photon incident event; and (2) (a) a detector response. Using the model, (b) the incident spectrum, and (c) the parameter vector settings to determine a plurality of component spectra each corresponding to one of the individual probabilities of different pileup events; ) Summing multiple component spectra to produce an output spectrum (also referred to as a composite spectrum); and (4) output spectrum. And (5) updating at least one of the values of the parameter vector, and (6) a parameter vector for optimizing the cost function. Including a processing unit configured to repeat the steps of determining, summing, calculating, and updating until a stop criterion is met.

  According to another embodiment, a method is provided for determining an output spectrum from a parameter vector comprising a plurality of parameters of a detector pileup model of a photon counting detector. Here, the detector pile-up model is used for pile-up correction for an X-ray CT apparatus, and the method is (1) dead time, single photon incident event probability, two photon Setting a plurality of parameter values including a probability of an incident event and an individual probability of different pileup events including a probability of at least a three-photon incident event; (2) (a) a response model of the detector; b) determining the plurality of component spectra using the incident spectrum and (c) the set value of the parameter vector. Here, each component spectrum corresponds to one of the individual probabilities of different pile-up events, and the step of determining is as one of the plurality of component spectra as a single photon incident event A first component spectrum is determined for the first component spectrum, and the first component spectrum is determined as Equation (3) below.

Here, S ₀ (E) is determined from the detected energy E, and the energy E is defined as the following formula (4).

Here, in Equations (3) and (4), S _in is the incident spectrum, E ₀ is the incident energy, z ₀ is the interference point, n is the incidence count rate, μ _CZT (E) is the linear attenuation value, τ _d is the dead time, ν _P is the output voltage of the preamplifier, and χ ₀ is the probability of a single photon incident event. The method further includes (3) adding a plurality of component spectra to generate an output spectrum.

  Hereinafter, an example of the above embodiment will be described in detail with reference to FIGS. As described above, the X-ray CT apparatus according to the present application is configured to improve the accuracy of pile-up correction. The photon-counting detector provided in the X-ray CT apparatus has high sensitivity and quantitativeness by counting each X-ray photon. However, the photon counting detector has a dead time during which processing for one photon cannot be performed for another photon, and even if another photon enters the detector during this time, it can handle it accurately. I can't. In the prior art, correction using a fixed dead time is performed for such pile-up. However, the dead time described above varies depending on the material of the detector, variations in the manufacturing process of the detection element, the size of the detection element, and the like.

For example, the dead time (˜100 ns) is determined by the type of semiconductor (for example, CZT or CdTe), the thickness, and the readout circuit as the material of the detection element, and at a high X-ray flux (˜10 ⁸ cps / mm ² ). Pile-up can be very severe and as a result, the measured spectral signal can be distorted. The distorted spectral signal will cause artifacts in the reconstructed image. Such dead time is not constant for a given readout circuit, depending on the position of pulse (electron-hole pair) formation within the detector cell. Therefore, the X-ray CT apparatus according to the present embodiment generates a detector model that corrects the influence of pileup based on various characteristics of the detection element, and corrects the measured spectrum to correct pileup. Improve accuracy and improve image quality.

Hereinafter, description will be given with reference to the drawings. FIG. 1 is a diagram illustrating an example of the configuration of the X-ray CT apparatus according to the present embodiment. Here, FIG. 1 shows a detector pileup model 10 that receives an incident spectrum S _in (E), a count rate, and a parameter vector a. The detector pileup model 10 is also described as a generation unit. The detector pileup model 10 generates an output spectrum (also referred to as a combined spectrum) S _out (E; a) measured by simulation based on the received value. Specifically, the detector pile-up model 10 is based on an incident spectrum that is an X-ray spectrum incident on the X-ray detector, a response model for the X-ray of the X-ray detector, and a parameter vector. Generate a composite spectrum. Hereinafter, the process of determining the output spectrum S _out (E; a) measured by simulation will be described in more detail.

As shown in FIG. 1, the model parameter estimation device 20 compares the output spectrum S _out (E; a) measured in the simulation with the actually measured measurement spectrum S _M (E) to determine a predetermined cost. The parameter vector a is updated so that the function can be minimized. The updated parameter vector a is fed back to the detector pileup model 10, and the detector pileup model 10 generates an output spectrum S _out (E; a) that is newly measured in the simulation. This process is continued until a predetermined number of iterations or the change of the parameter vector a falls below a predetermined threshold. Here, as will be described later, the model parameter estimation device 20 performs, for example, an exhaustive search within a predetermined range for the parameter vector a or a nonlinear least square method for finding the optimal parameter vector a. Can be applied. Each optimum parameter vector a is found for each photon counting detector. The model parameter estimation device 20 is also described as a generation control unit.

The incident spectrum S _in (E) is calculated for each photon-counting detector (PCD) of the scanner (all manufacturers are required to calculate the output from their X-ray tube). Have a model) or measured values (measured using an optimal reference spectrometer detector, eg, a high purity germanium spectrometer). The measured spectrum S _M is an output spectrum from each PCD corresponding to each incident spectrum.

The parameter vector a is a dead time value τ _d and, for example, a time threshold T that determines whether the two-photon incident event is a peak pileup event or a tail pileup event (despite being a threshold, This time threshold T is applied to determine whether peak or tail pile-up events occur in any pile-up order), different numbers of incident photons χ ₀ , χ ₁ ^p , χ ₁ ^t , Χ ₂ ^p , χ ₂ ^t and other probabilities. Here, the peak pile-up event is an event (first two-photon incident event) in which two photons are incident so that the other spectrum overlaps a peak in one spectrum in the two-photon incident event. The tail pile-up event is an event (second two-photon incident event) in which two photons are incident so that the other spectrum overlaps after the peak in one spectrum in the two-photon incident event. For example, χ ₀ is the probability of a single photon incident event, χ ₁ ^p is the probability of a peak two-photon incident pileup event, χ ₁ ^t is the probability of a tail two-photon incident pileup event, and χ ₂ ^p is a three-photon incident For example, the probability of a peak pile-up event. In practice, the contribution of higher order spectra decreases rapidly with increasing order, so in most embodiments these spectra can be ignored when calculating the summed spectra. Note that the sum of the individual probabilities is equal to or less than 1.

The detector pileup model 10 calculates S _out (E) from S _in (E) and the parameter a by the method shown in FIG. FIG. 2 is a flowchart showing a procedure of processing by the detector pileup model 10 according to the present embodiment.

As shown in FIG. 2, the detector pile-up model 10 first receives a parameter vector a and an incident spectrum S _in (E) that includes an upper dead time τ _d and individual probabilities for different numbers of incident photons χ. Or it is set (step S200).

Next, the detector pileup model 10 calculates the first component spectrum S ₀ (E) corresponding to the single photon incident event according to the Poisson distribution using S _in (E) and the parameter vector a. (Step S210). Here, if the single photon incidence event is estimated by Poisson distribution, the influence of pixel weighting potential, depth of interaction, ballistic deficit, and space charge Is included in the calculation of S ₁ (E). If Poisson distribution is used, it is reflected in terms e ^-nτd , ne ^-nτd , 1/2 n ² e ^-nτd, etc. included in the component spectrum equations (S ₀ , S ₁ , S _2, etc.) described later. It becomes. Hereinafter, an example of the calculation of the first component spectrum will be described.

  First, the above-described weighting potential is defined as the following formula (5).

Here, in Equation (5), z indicates the distance between the CZT point and the cathode, z ₀ indicates the point at which the X-ray photon is converted into an electron-hole pair, and t _TOF is the generated electron. Represents the time for the air to float from the interference point z ₀ to the anode of the detector. Α represents a model parameter describing the weighted potential distribution of the detector, L represents the thickness of the detector, and ν _e represents the floating speed of the electron carrier in the photon counting detector.

  The basic equation for the above ballistic defect is shown by the following mathematical formula (6).

Here, in Equation (6), E represents the incident energy, K represents the front end gain (a constant for a given readout configuration), τ _p represents the time constant of the preamplifier, and ν _p (t) indicates the output voltage of the preamplifier.

In the case of 0 ≦ t ≦ t _TOF , the preamplifier output can be expressed by the following equation (7) from the basic equation.

However, ν ⁰ is determined by the initial condition shown in the following mathematical formula (8).

  Then, the following mathematical formula (9) is obtained by inserting the weighted potential equation represented by the mathematical formula (5) into the mathematical formula (7).

  And the following numerical formula (10) is obtained by calculating the integral of numerical formula (9).

Furthermore, when the initial conditions described above are applied, the constant ν ⁰ can be expressed as the following formula (11).

  However, Formula (11) is the following Formula (12).

  Here, when the following formula (13) is satisfied, the generated electrons reach the anode of the detector, and the preamplifier output reaches the maximum.

  That is, the following formula (14) is obtained.

Note that t _TOF will be different if the space charge cannot be ignored.

Here, in the case of t> t _TOF , after t _TOF , the signal acquisition is completed, and the output amplitude is exponentially attenuated by the front-end circuit time constant τ _p . That is, the following formula (15) is obtained.

As described above, the formulation of ν _p (t) depends on the interference point z ₀ and the incident energy E ₀ . Therefore, the applicants indicate it as the following formula (16). In the following, in order to simplify the display, E ₀ in ν _p (t) is omitted. In the following, the following equation (17) is also applied to define the flight time and the interference depth of the event j.

  Hereinafter, calculation of the first component spectrum will be described. When there is no pileup, the detector pileup model 10 calculates the first component spectrum as follows. Here, the detected energy E is defined as the following formula (18), and the first component spectrum is expressed as the following formula (19).

However, the integral in Equation (19) spreads over the entire volume depending on the energy state. Further, when the flexible dead time approximates to the true dead time, the detection probability is χ ₀ to ¹ . In the above equation, n is the incident count rate and μ _CZT (E) is the linear attenuation of CZT at energy E.

Returning to FIG. 2, the detector pile-up model 10 then converts the second component spectrum S ₁ (E) corresponding to the two-photon incident event including the peak pile-up event and the tail pile-up event to S _in (E ) And the parameter vector a (step S220). Here, in the case of a two-photon incident event, if the time interval between incident events is smaller than the threshold T, it is determined that a peak pile-up event has occurred. If the time interval is greater than the threshold T, a tail pile-up event has occurred. Is determined. The threshold T is included in the parameter vector a.

  First, in the case of a peak pile-up event, energy is defined as the following formula (20).

  And a peak component spectrum is shown like following Numerical formula (21).

  When the flexible dead time approximates to the true dead time, the detection probability is expressed by the following formula (22).

  Next, in the case of a tail pile-up event, the first peak energy is defined as the following formula (23).

  And a component spectrum is shown like following Numerical formula (24).

  Further, the second peak energy is defined as the following formula (25).

  And a component spectrum is shown like following Numerical formula (26).

When the flexible dead time approximates to the true dead time, the detection probability is expressed by the following formula (27). Detector pileup model 10 then adds the peak and tail pileup component spectra to equation S ₁ (E).

Returning to FIG. 2, the detector pileup model 10 next includes a third component spectrum S ₂ (E) for multiple (at least 3 photon or more) photon incident events including peak and tail pileup events. Is calculated using S _in (E) and the parameter vector a (step S230).

  Here, in the case of three-photon pileup, energy is defined as in the following formula (28) with respect to peak pileup.

  And a peak component spectrum is shown like following Numerical formula (29).

  When the flexible dead time approximates to the true dead time, the detection probability is expressed by Equation (30). The approximate expression is the following expression (31).

  However, in the formula (31), the following formula (32) is satisfied, and N indicates a normalization factor.

  Next, for tail pileup, or for mixed pileups where tails and peaks are mixed, the calculation is similar to the two-photon pileup calculation, but more combinations are considered. For example, in the case of the first combination (0-1-2), the energy is defined as the following mathematical formula (33).

  In the case of the second combination ((01) -2), the energy is defined as the following mathematical formula (34).

  Other combinations such as ((02) -1) and ((12) -0) are similar to the second combination.

  Here, in the case of tail pileup, or in the case of mixed pileup where tails and peaks are mixed, the corresponding formula can be easily obtained by generalizing the formula used for two-photon pileup. Can do. In one embodiment, tail pileup is ignored using, for example, an approximation for peak pileup.

In another embodiment, a three-photon event is treated as a two-photon event between (1) a two-photon event (primary pileup) and a single photon event (no pileup). In this case, the component spectrum is calculated from the component spectrum of the two-photon event and the component spectrum without pileup. One component spectrum is substituted into one term S _in (E) of the two-photon event equation S ₁ (E), and at the same time, the other component spectrum is substituted into the other S _in (E) of the same equation. This technique can be extended to higher pileup events.

Returning to FIG. 2, the detector pileup model 10 then sums the calculated component spectra S _i (E), i = 0, 1, 2, etc. to produce S _out (E; a). (Step S240). FIG. 4 is a diagram showing the sum of component spectra obtained by the detector pileup model according to the present embodiment. Here, P0 indicates the first component spectrum S ₀ (E) corresponding to the single photon incidence event, and P1 is the sum of the first and second component spectra S ₀ (E) + S ₁ (E). Indicates. P2 corresponds to S _out (E; a) and indicates the sum of the first, second, and third component spectra.

  FIG. 5 is a diagram showing the sum of component spectra calculated with a constant detection probability. As shown in FIG. 5, when a certain detection probability is used, the effect of pileup is overestimated. However, as shown in FIG. 4, the spectrum calculated by the detector pileup model 10 is a spectrum that takes into account the probability of each pileup.

Returning to FIG. 1, the model parameter estimation device 20 can compare the output spectrum S _out (E; a) measured by simulation with the actually measured spectrum to minimize the predetermined cost function. The parameter vector a is updated as follows. FIG. 3 is a flowchart showing a processing procedure by the model parameter estimation device 20 according to the present embodiment.

  For example, as shown in FIG. 3, the model parameter estimation device 20 defines an appropriate range for each of the parameters of the parameter vector a, and calculates the cost function Ψ (a), for example, (Step S300).

That is, the model parameter estimation device 20 uses a cost function indicating the degree of difference between the output spectrum S _out (E; a) and the measured spectrum S _M (E). The cost function is not limited to the mathematical formula (35), and another appropriate cost function may be used.

Then, the model parameter estimation device 20 calculates the value of the cost function based on the received value of S _out (E, a) and the measured spectrum S _M (E) (step S310). Further, the model parameter estimation device 20 stores the value of the cost function Ψ (a) in association with the current parameter vector a.

  Thereafter, the model parameter estimation device 20 determines whether or not the stop criterion is satisfied (step S320). For example, when the change in the parameter vector a is determined and the change in the parameter vector a falls below a predetermined threshold, the model parameter estimation device 20 ends the process. On the other hand, if the stop criterion is not satisfied, the process continues to step S330. Alternatively, when the number of repetitions of updating the parameter vector a exceeds a predetermined number, the process is terminated. Note that other combinations of stopping criteria such as stopping when the number of iterations exceeds a predetermined number or when the change of the parameter vector a falls below a predetermined threshold may be used.

  Then, the model parameter estimation device 20 updates the parameter vector a by a predetermined optimization method (Step S330). For example, the model parameter estimation device 20 updates the parameter vector a by an exhaustive search algorithm. In such a case, the parameter vector a is updated by a predetermined systematic method within a range defined for each parameter. Alternatively, the model parameter estimation device 20 can use a nonlinear least squares fitting method such as the Levenberg Marcus method. In such a case, the gradient of the cost function is estimated. Note that another optimization method can be used to minimize the cost function.

Then, the model parameter estimation device 20 feeds back the updated parameter vector a to the detector pileup model (step S340). The detector pileup model calculates a new S _out (E, a) using the updated parameter vector a and returns to step S310. Here, in step S310, a new S _out (E, a) value is received and the cost function is recalculated using the same measured spectrum S _M (E).

In another embodiment, one or more of the values of a parameter, such as dead time τ _d, can be directly derived from the detector placement and readout electronics configuration. Further, in another embodiment, a combination of the direct calculation method and the empirical method described above with respect to FIGS. For example, some of the parameter values can be calculated directly, and the remaining values can be determined empirically. Alternatively, the initial estimate of the parameter value can be calculated directly and used as the initial value in the above empirical method of reducing the computational burden.

  Once the optimal parameters of the detector pileup model are determined as indicated above, various algorithms for spectral correction using the model can be used. That is, the value of the incident spectrum can be obtained based on the measured spectrum. For example, (1) a gradient-based method for minimizing the cost function, (2) a search-based method for finding an incident spectrum within a given search region so that the cost function can be minimized, and (3) a response. Function-based iterative methods.

  For example, in the response function-based method, in the case of a linear example without pileup, a detector pileup model (output spectrum) is defined or modeled as the following Expression (36).

  Here, in Equation (36), R (E, E ′) represents the response matrix of the detector model and includes the determined parameter vector a. The response matrix can be defined as the following formula (37) from the formula of the component spectrum when there is no pileup.

The incident spectrum S _in (E) is obtained by repetitively solving the following mathematical formula (38).

  Next, in the case of a non-linear example with pile-up, a detector pile-up model (output spectrum) is defined or modeled as the following formula (39).

Here, in Equation (39), R ₂ (E, E ′, E ″) is a two-photon response matrix of the detector model, and is determined using the parameter vector a. The response matrix can be defined as the following equation (40) from the component spectrum equation for the two-photon peak pileup.

  Similarly, a two-photon response matrix for tail pile-up is defined as in Equation (41) below. The overall two-photon response matrix is shown as the following formula (42).

The incident spectrum S _in (E) is obtained by repetitively solving the following mathematical formula (43).

  Note that these two equations can be easily expanded to include multiple (three or more) photon response matrices representing higher order pileups.

  The above embodiments for determining the detector pileup model include many advantages over conventional pileup correction methods. For example, the embodiments described above correspond to flexible dead time, and can correspond to varying actual dead time in the photon counting detector, as well as flexible pulse shapes. Furthermore, the above-described embodiments can include individual detection probabilities for different numbers of incident photons instead of the constant detection probabilities used in conventional methods.

The above model equations are based on specific weighting potentials and ballistic deficit equations. For example, weighted potentials and ballistic deficit equations are used to show the only example where the computation of ν _p (t) has a closed form. Other equations can be used and the component spectrum can be computed as well (the probability method is still valid), but with a different ν _p (t) function that can no longer have a closed-form solution.

  The pulse shape is also incorporated into the weighting potential and ballistic deficit equations. Thus, different pulse shapes yield different equations.

  Furthermore, the disclosed embodiments model realistic pixel weighting potential, interference depth, ballistic deficit, and space charge. The embodiment described above shows one example of a weighting potential and a ballistic defect model. However, in other embodiments, other models of signal guidance and detector response determined by the detector configuration can be incorporated into the method.

  FIG. 6 is a diagram showing an X-ray CT apparatus according to the present embodiment. The X-ray CT apparatus of FIG. 6 includes an X-ray tube 1, a filter and collimator 2, and a detector 3. The X-ray CT apparatus also includes a sparse fixed energy identification (eg, photon counting) detector arranged at a radius different from the radius of the third generation detector, for example, as shown by the black rectangle in FIG. Including. The X-ray CT apparatus further includes mechanical and electrical components such as a gantry motor and a controller 4, and can control the rotation of the gantry, the X-ray source, and the subject bed. . The X-ray CT apparatus also includes a data acquisition system 5 and a processing apparatus 6 that can generate a CT image based on projection (field of view) data acquired by the data acquisition system. For example, the processing device 6 includes a reconstruction processing device to reconstruct a spectral CT image. That is, the reconstruction processing device included in the processing device generates a correction spectrum in which the pile-up event is corrected based on the combined spectrum whose cost function is below a predetermined threshold, and reconstructs an image based on the generated correction spectrum. To do.

  Here, the processor is programmed to determine the parameters of the detector pileup model and to execute a method for performing pileup correction for each photon counting detector, as described above. Further, the processing device and the data acquisition system use the storage unit 7. The storage unit 7 is configured to store, for example, a computer program, data obtained from a detector, a detector pileup model, and a reconstructed image.

  In one embodiment, the processing device includes (1) dead time, single photon incident event probability, two photon incident event probability, and individual pileup event individual probabilities including at least three photon incident event probability. A setting step for setting a plurality of parameter values including: (2) (a) a response model of the detector, (b) an incident spectrum, and (c) a setting value of the parameter vector, and different pile-up events A determination step for determining a plurality of component spectra respectively corresponding to one of the individual probabilities of (2), and (3) a generation step for summing the plurality of component spectra to generate an output spectrum (also referred to as a composite spectrum); (4) Calculation for calculating the value of the cost function based on the output spectrum and the measured measurement spectrum And (5) an update step that updates at least one of the values of the parameter vector; and (6) a decision, sum until a stop criterion is met so that a parameter vector that optimizes the cost function can be determined. Iterating steps for repeating the calculating and updating steps.

  As will be apparent to those skilled in the art, the processing unit 6 may be an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), or other combined programmable logic circuit. It includes a CPU that can be implemented as a separate logic gate, such as (Complex Programmable Logic Device: CPLD). The implementation of FPGA or CPLD is VHDL (VHSIC (Very High Speed Integrated Circuit) Hardware Description Language), Verilog (Verilog), or any other hardware description language. Good. The code may be stored directly in the FPGA or CPLD or as a separate electronic memory in the electronic memory. Further, the memory includes ROM (Read Only Memory: Read Only Memory), EPROM (Electrically Programmable Read Only Memory: Electrically Programmable Read Only Memory), EEPROM (Electrically Erasable Programmable Read Only Memory). ) Or flash (FLASH) memory or the like. The memory may also be volatile, such as static RAM (Random Access Memory) or dynamic RAM. A processing device such as a microcontroller or microprocessor may be provided to manage the electronic memory and the interaction between the FPGA or CPLD and the memory.

  Alternatively, the CPU of the reconstruction processing device can execute a computer program that includes a set of computer-readable instructions that perform the functions described herein, where the program is stored in the non-transitory electronic memory and hard disk device described above. Either or both, CD (Compact Disc), DVD (Digital Versatile Disc), flash drive or any other known storage medium. In addition, computer-readable instructions include Xeon processors from Intel, USA, or Opteron processors from AMD (Advanced Micro Devices), and Microsoft VISTA, UNIX ( Utility applications, background daemons, or operating systems that run with processing devices such as operating systems such as registered trademark, Solaris, LINUX®, Apple, MAC-OS, and other operating systems known to those skilled in the art It is good to provide as a component of these, or those combination.

  Once processed by the pre-reconstruction processor, the processed signal is passed to a reconstruction processor that is configured to generate a CT image. The image is stored in the memory and / or displayed on the display unit. As will be apparent to those skilled in the art, the memory may be a hard disk drive, CD-ROM drive, DVD drive, flash drive, RAM, ROM, or any other electronic storage known in the art. The display unit includes an LCD (Liquid Crystal Display) display device, a CRT (Cathode Ray Tube) display device, a plasma display device, an OLED (Organic Light Emitting Display), and an LED (Light Emitting Display). A light emitting display device) or any other display device known in the art. As such, the descriptions of storage and display provided herein are merely examples and in no way limit the scope of this advancement.

  As described above, according to the present embodiment, the accuracy of pile-up correction can be improved.

  Although several embodiments of the present invention have been described, these embodiments are presented by way of example and are not intended to limit the scope of the invention. These embodiments can be implemented in various other forms, and various omissions, replacements, and changes can be made without departing from the spirit of the invention. These embodiments and modifications thereof are included in the scope of the present invention and the gist thereof, and are also included in the invention described in the claims and the equivalent scope thereof.

Claims (10)

An X-ray tube that generates X-rays;
An X-ray detector that detects X-ray photons generated from the X-ray tube and outputs a measurement spectrum;
A generating unit that generates a synthetic spectrum based on a parameter vector including a parameter related to a probability of a pile-up event and a parameter related to a dead time of the X-ray detector;
A parameter vector including a parameter related to the probability of the pile-up event is changed so that the difference between the measurement spectrum output by the X-ray detector and the synthesized spectrum generated by the generation unit is below a predetermined threshold. A generation control unit that controls the generation unit to generate the composite spectrum,
A reconstructing unit that generates a correction spectrum in which the pile-up event is corrected based on a combined spectrum in which the degree of difference falls below a predetermined threshold, and reconstructs an image based on the generated correction spectrum;
An X-ray computed tomography apparatus comprising:   The generation unit generates the combined spectrum based on an incident spectrum that is an X-ray spectrum incident on the X-ray detector, a response model of the X-ray detector to the X-ray, and the parameter vector. The X-ray computed tomography apparatus according to claim 1.   The X-ray computer according to claim 1 or 2, wherein the parameters related to the probability of the pile-up event include a probability of a single photon incident event, a probability of a two photon incident event, and a probability of an incident event of at least three photons. Tomography equipment.   The X-ray computed tomography apparatus according to claim 1, wherein the parameter related to the dead time is set based on characteristics of each detection element of the X-ray detector. In the two-photon incident event, the two-photon incident event includes a first two-photon incident event in which two photons are incident so that a second spectrum overlaps a peak in one spectrum, and a peak in one spectrum. And further including a time threshold for distinguishing from a second two-photon incident event in which two photons are incident so that the other spectrum overlaps,
4. The X-ray computed tomography apparatus according to claim 3, wherein the generation unit generates a combined spectrum including the first two-photon incident event and the second two-photon incident event in the two-photon incident event. .   The generation control unit controls the generation spectrum to generate the synthetic spectrum until the degree of difference reaches less than a predetermined threshold or until the number of generations of the synthetic spectrum by the generation unit reaches a predetermined number. The X-ray computed tomography apparatus described.   The X-ray computed tomography apparatus according to claim 1, wherein the parameter vector is updated by a non-linear least square method. An X-ray tube that generates X-rays;
An X-ray detector that detects X-ray photons generated from the X-ray tube and outputs a measurement spectrum;
A parameter vector comprising a single-photon incident event probability, a two-photon incident event probability, and a parameter related to a pile-up event probability including at least a three-photon incident event probability and a parameter related to the dead time of the X-ray detector. A generating unit for generating a composite spectrum based on
A parameter including a parameter relating to the probability of the pile-up event so as to generate a synthetic spectrum in which the degree of difference between the measured spectrum output by the X-ray detector and the synthetic spectrum generated by the generation unit is lower than a predetermined threshold A generation control unit that controls the change of the vector ;
A reconstructing unit that generates a correction spectrum in which the pile-up event is corrected based on a combined spectrum in which the degree of difference falls below a predetermined threshold, and reconstructs an image based on the generated correction spectrum;
An X-ray computed tomography apparatus comprising: Pile-up correction executed by an X-ray computed tomography apparatus including an X-ray tube that generates X-rays and an X-ray detector that detects X-ray photons generated from the X-ray tube and outputs a measurement spectrum A method,
Generating a composite spectrum based on a parameter vector including a parameter relating to a probability of a pile-up event and a parameter relating to a dead time of the X-ray detector;
The synthesis is performed while changing a parameter vector including a parameter related to the probability of the pile-up event so that the degree of difference between the measurement spectrum output by the X-ray detector and the generated synthesized spectrum is below a predetermined threshold. Control to generate spectrum,
Generating a corrected spectrum in which the pile-up event is corrected based on a combined spectrum in which the degree of difference falls below a predetermined threshold, and reconstructing an image based on the generated corrected spectrum;
A correction method including the above. Pile-up correction executed by an X-ray computed tomography apparatus including an X-ray tube that generates X-rays and an X-ray detector that detects X-ray photons generated from the X-ray tube and outputs a measurement spectrum A method,
A parameter vector comprising a single-photon incident event probability, a two-photon incident event probability, and a parameter related to a pile-up event probability including at least a three-photon incident event probability and a parameter related to the dead time of the X-ray detector. To generate a composite spectrum based on
Change in parameter vector including parameters related to the probability of the pile-up event so as to generate a composite spectrum in which the difference between the measured spectrum output by the X-ray detector and the generated composite spectrum is below a predetermined threshold controls,
Generating a corrected spectrum in which the pile-up event is corrected based on a combined spectrum in which the degree of difference falls below a predetermined threshold, and reconstructing an image based on the generated corrected spectrum;
A correction method including the above.

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