Method and apparatus for determining PCD output model in computed tomography imaging system

Abstract

To provide a method for determining a model characterizing an output from a photon-counting detector (PCD) used in a computed tomography (CT) system.SOLUTION: A PCD has a plurality of pixels. A method includes constructing a PCD output model that has a plurality of model parameters including a first model parameter set. The first model parameter set is dependent on an incident count rate on the PCD, and dependent on a pixel position in the PCD. The method also includes: receiving calibration data acquired by scanning a plurality of combinations of basis materials, under a plurality of incident count rates; and estimating the plurality of model parameters based on the received calibration data.SELECTED DRAWING: None

Description

[Technical field]

[0001] The embodiments disclosed herein and in the drawings relate to X-ray Computed Tomography (CT) imaging systems based on Photon-Counting Detectors (PCDs). In particular, this application relates to determining a model for characterizing the output of PCDs used in CT imaging systems. [Background technology]

[0002] PCD-based CT offers many clinical advantages over conventional energy-integrated detector CT due to its energy discrimination capability. However, the response of PCDs to different X-ray energy levels is not linear, and the X-ray spectrum is distorted by several factors, such as charge sharing (CS) and pulse pileup (PP). To compensate or correct the spectral distortion and fully realize the benefits of PCDs, it is important to characterize the PCD output.

[0003] Approaches to characterize PCD data are database- or model-based, and database-based approaches are either calibration-based or deep learning-based. Through a calibration process, calibration-based methods estimate parameters of empirical functions such as polynomials for the forward process (i.e., calculating expected values ​​of measured data from a set of variables (e.g., thickness of attenuating material)) or inverse process (returning a set of variables from measured data). Deep learning-based methods use many more parameters than calibration-based methods and determine mapping functions from training data. These database approaches are simple and can be accurate if the scanning conditions used for calibration or training match the scanning conditions of interest. However, they require a lot of effort because a lot of calibration or training data is required and their accuracy in untested conditions is uncertain.

[0004] In contrast, model-based methods analytically interpret the physical detection process, including charge sharing and pulse pile-up, and relate upstream variables, such as the thickness of the attenuating material, to expected PCD data. These methods can handle untested conditions, provided the model parameters are estimated and the model behavior is verified. However, it is very difficult to develop models that match the data of physical PCDs well. A handful of models have been evaluated for physical PCDs, but even these models show visual mismatch with the output of physical PCDs when both charge sharing and pulse pile-up are present. Two challenges with model-based methods are the remaining model-data mismatch and pixel-to-pixel variability.

[0005] Therefore, there is a need to provide a method to mitigate the model-data mismatch problem and create a more enhanced PCD output model. Summary of the Invention [Means for solving the problem]

[0006] One embodiment of the present application relates to a method for determining a model characterizing an output from a photon counting detector (PCD) used in a computed tomography (CT) system. The PCD has a plurality of pixels. The method includes constructing a PCD output model having a plurality of model parameters including a first model parameter set. The first model parameter set is dependent on an incident count rate on the PCD and dependent on a pixel location within the PCD. The method also includes receiving calibration data acquired by scanning a plurality of basis material combinations under a plurality of incident count rates. The method further includes estimating the plurality of model parameters based on the received calibration data.

[0007] Another embodiment of the present application relates to an apparatus for determining a model characterizing an output from a photon counting detector (PCD) used in a computed tomography (CT) system. The PCD has a plurality of pixels. The apparatus includes a processing circuit configured to construct a PCD output model having a plurality of model parameters including a first model parameter set, the first model parameter set being dependent on an incident count rate on the PCD and dependent on a pixel location within the PCD. The processing circuit is further configured to receive calibration data obtained by scanning a plurality of basis material combinations under a plurality of incident count rates. The processing circuit is also configured to estimate the plurality of model parameters based on the received calibration data.

[0008] A further embodiment of the present application relates to a non-transitory computer readable medium having stored thereon a program that, when executed by a processing circuit, causes the processing circuit to perform a method for determining a model characterizing an output from a photon counting detector (PCD) used in a computed tomography (CT) system. The PCD has a plurality of pixels. The method includes constructing a PCD output model having a plurality of model parameters including a first model parameter set. The first model parameter set is dependent on an incident count rate on the PCD and dependent on a pixel location within the PCD. The method also includes receiving calibration data obtained by scanning a combination of a plurality of basis materials under a plurality of incident count rates. The method further includes estimating the plurality of model parameters based on the received calibration data. [Brief description of the drawings]

[0009] [Figure 1] 1 shows a flowchart of a PCD model development process 100 according to an embodiment of the present application. [Diagram 2] 2 shows a flow chart of a calibration process 200 for a PCD output model according to an embodiment of the present application. [Diagram 3] The structure of a PCD is shown, which detects X-rays that are emitted from an X-ray tube and pass through an imaging target. [Figure 4A] A scatter plot of the 30 data points used for model parameter estimation (26 data points) and validation (4 data points) is shown plotted across water thickness, aluminum thickness, and tube current values. [Figure 4B] The initial 120 kVp spectrum and the most attenuated spectrum are shown. [Figure 5A] The measured count rates and the count rates from the modified cascade PCD model using the model parameters obtained in step 1 are shown. [Figure 5B] The fitting results of the global threshold function, Eglob(a,cb), obtained in step 3 are shown. [Figure 6] The measured PCD data and output of the three PCD models are shown for the lowest count rate condition of the test data of 10 mA, 16 cm of water, and 0.5 cm of aluminum. [Figure 7] Measured PCD data at highest count rate conditions with a blank scan at 100 mA and the output of the three PCD models are shown. [Figure 8A] For each bin, we show the Mean Absolute Percentage Error (MAPE, left axis) of the three models calculated on each of the four test data, and the coefficient of variation (CV, dashed line, right axis) of the measured data. [Figure 8B] For each bin, we show the Mean Absolute Percentage Error (MAPE, left axis) of the three models calculated on each of the four test data, and the coefficient of variation (CV, dashed line, right axis) of the measured data. [Figure 8C] For each bin, we show the Mean Absolute Percentage Error (MAPE, left axis) of the three models calculated on each of the four test data, and the coefficient of variation (CV, dashed line, right axis) of the measured data. [Figure 8D]For each bin, we show the Mean Absolute Percentage Error (MAPE, left axis) of the three models calculated on each of the four test data, and the coefficient of variation (CV, dashed line, right axis) of the measured data. [Figure 9] The MAPEs of the three PCD models calculated with respect to the incident count rate of the entire test data are shown. [Figure 10] 1 illustrates an example of a photon-counting CT scanner system that can incorporate the technology disclosed herein. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0010] Embodiments or examples for implementing various aspects of the present application may be described in the following sections. Specific examples of components and arrangements are described below to simplify the present application. Of course, these are merely examples and are not intended to be limiting.

[0011] The order of description of the different steps described herein is presented for clarity. In general, these steps can be performed in any suitable order. Moreover, although each of the different features, techniques, configurations, etc. of this specification may be discussed in different places in this application, it is intended that each of the concepts can be performed independently of each other or in combination with each other. Thus, this application can be embodied and contemplated in many different ways.

[0012] Additionally, as used herein, the words "a," "an," and the like generally mean "one or more" unless otherwise specified.

[0013] To overcome the aforementioned challenges, this application introduces a method and apparatus for the development of a high-precision PCD output model. By incorporating a count-rate dependent threshold energy function, the method and apparatus effectively address the global model-data mismatch of the cascade model as well as pixel-to-pixel variations. The resulting PCD output model provides an accurate estimation of the physical PCD output.

[0014] The PCD output model shows excellent agreement with the measured PCD data, with the mean absolute percent error (MAPE) being less than 5% for all test data and less than 2% for the majority of datasets. On average, the MAPE across all bins ranges from 1.1 to 2.4%. The model is expected to contribute significantly to applications where pixel-wise accuracy is critical.

[0015] FIG. 1 shows a flowchart of a PCD model development process 100 according to an embodiment of the present application. In step S110, a cascaded PCD output model is constructed. The model may include a plurality of model parameters, including a condition-dependent and pixel-specific first parameter set. In step S120, a plurality of model parameters of the PCT output model may be estimated through a calibration process based on a calibration data set. Optionally, in step S130, the performance of the PCT output model with the estimated parameters may be verified based on a validation data set. The developed model may be used to simulate the output of a PCD and may accurately represent the behavior of the PCD. Furthermore, the developed model may be used to correct or compensate for spectral distortions in measured PCD output data, ensuring reliable and accurate measurement results.

[0016] FIG. 2 shows a flow chart of a calibration process 200 of a PCD output model according to an embodiment of the present application. The process begins at step S210, where calibration data sets are obtained. These data sets, along with a validation data set used in optional step S130 of FIG. 1, may be obtained from tests conducted across various combinations of basis materials and multiple x-ray tube currents. At step S210, initial values ​​of multiple model parameters may be estimated based on the received calibration data. At step S230, a condition-dependent sub-parameter set of the first parameter set may be estimated, and at step S240, a pixel-specific sub-parameter set of the first parameter set may be estimated.

[0017] Details of each process shown in Figures 1 and 2 can be found in the following sections.

[0018] I. Cascade PCD Output Model The cascade PCD output model describes four processes that sequentially change the X-ray spectrum and output the final spectrum: (1) Beer's law attenuation, (2) charge sharing effects that can be estimated from Monte Carlo simulations, (3) pulse pile-up effects, and (4) the energy binning process.

[0019] Figure 3 shows the structure of a PCD that detects X-rays emitted from an X-ray tube and transmitted through an imaging target. Let n be the X-ray spectrum vector, and its element n E is the energy E, E∈{1,2,…,E max The output y of the cascade PCD model represents the number of photons in a virtual 1 keV energy window at 1 keV. 0 It can be calculated from the following:

[0020]

number

[0021] where v denotes the set of basis material thickness vectors (mm), τ is the detector dead time (sec), E ,thr is the threshold energy vector (keV), E thr =(E thr,1 ,…,E thr,B ) T where B is the number of energy bins in the PCD and the superscript T denotes transposition. The initial spectrum vector n 0 is 0 =(k 0 ×dA×l) / R 2 ×S 0 can be calculated as follows, where S 0 means the probability mass function of the X-ray spectrum, and k 0 is the X-ray photon output rate (counts / s / mA / mm at 1 m from the X-ray focus) 2 ), dA is the detector pixel area (mm 2 ), l is the tube current (mA), and R is the distance from the source to the detector (m). Among all the parameters, k 0 and τ are the only parameters in the original model that need to be estimated by calibration. A , Ψ CS , Ψ PP , and Ψ B The following explains this.

[0022] A. Decay operator Ψ A Operator Ψ A uses Beer's law to calculate the attenuated spectrum vector n A is calculated as follows:

[0023]

number

[0024] Here, M(v(vector quantity)) is the damping matrix, M(v(vector quantity))=diag(exp(-μ 1 (vector quantity)v(vector quantity)),...,exp((-μ max (vector quantity)v(vector quantity)), where diag is the diagonal operator, μE (vector quantity)v(vector quantity)=μ 1,E v 1 +μ 2,E v 2 where μ E (Vector quantity) is the linear damping coefficient vector (mm -1 ), whose elements are the linear attenuation coefficients of the two basis materials at the X-ray energy E.

[0025] B. Charge sharing operator Ψ CS Operator Ψ CS is the spectrum vector after charge sharing, n CS Output.

[0026]

number

[0027] where H is a two-dimensional matrix that models the effect of CS, and each column of H represents the expected X-ray spectrum given one count input at a particular X-ray energy of the PCD. H can be obtained by Monte Carlo simulation.

[0028] The Monte Carlo simulation can include (i) photoelectric interaction, (ii) Compton scattering, and (iii) transmission without interaction. Post-interaction fluorescent X-ray emission can also be considered. H can include the effects of both spill-in and spill-out crosstalk from adjacent PCDs, including first-order interactions, second-order interactions, etc. Note that the sum of H for each column can be greater than 1 due to spill-in crosstalk.

[0029] C. Pulse pileup operator Ψ PP Operator Ψ PP is the input spectrum vector n CS and the detector dead time τ, the spectrum after pulse pile-up n PP Returns

[0030]

number

[0031] This can be expressed as a product of three probabilities as follows:

[0032]

number

[0033] where the subscript E refers to the Eth element of the spectrum vector or function output. A non-analytical detection model can be used, where Pr(rec|aτ) is the probability that an event is recorded given by

[0034]

number

[0035] Here, a is the incident count rate, a=Σ E_{thr,n} E_max Psi CS (Ψ A (n 0 ,v)). E thr、n is the threshold energy for noise cutoff, e.g. 10 keV.

[0036] Pr(m|rec) is the probability of an m-th pulse pile-up event given the recorded event of interest, and is given by:

[0037]

number

[0038] Finally, Pr(E|m) is the probability of the recorded energy E given an m-th order pulse pile-up event. The probabilities are calculated from the lowest order pulse pile-up (m=0) to higher orders. The recorded energy is assumed to be the maximum pulse height of the sum of triangular pulses, each with a weighted dead-time width and X-ray energy height.

[0039] D. Energy binning operator Ψ B

[0040] Operator Ψ B calculates the PCD output by integrating the spectral vector with a given threshold energy vector as follows:

[0041]

number

[0042] II. Global and local model parameters

[0043] Through testing the cascade PCD output model at various count rates, the following observations are made regarding the mismatch between the model and the data: (1) the global mismatch of the energy bin data is smaller at lower count rates and larger as the count rate increases, (2) the total counts show good agreement in the total count range investigated, and (3) there is a large pixel-to-pixel variation even at low count rates, with slight changes depending on the count rate, but it is reasonably consistent regardless of the count rate.

[0044] Observations (1)-(2) suggest the presence of count-rate dependent effects that the above cascade PCD model does not account for. These observations also suggest that the count-rate dependent effects may result from spectral distortion effects above a minimum threshold energy rather than from the total count rate. Observation (3) indicates that the local mismatch is mostly caused by count-rate independent effects.

[0045] From these observations, we can conclude that the causes of these two kinds of mismatches must be different from each other. The global mismatch could be caused either by baseline shifts that depend on the counting rate of the pulse train (i.e., effects that remain even when baseline restoration is employed), by a simple mismatch between the PP model and the actual effect of PP due to PCD, or by other unknown nonlinear spectral effects. The local mismatch could be due to a mismatch between H used in the CS model and the actual effect of CS, or by other unknown factors.

[0046] It is therefore advisable to address global and local mismatches separately, as not only their causes but also the possible future changes between the two mismatches may differ.

[0047] The above cascade PCD output model has five parameter sets, namely, S 0、 k 0、 H, τ, and E thr According to the implementation of this application, E thr can be optimized for the conditions. Note that this is not limiting, as H and / or τ can be optimized for conditions in other implementations.

[0048] A. Global threshold energy for global mismatch As mentioned above, the threshold energy E thr can be chosen as a count-rate dependent variable, which deviates from the calibrated value at very low count rates. The global change in threshold energy can be modeled using an exponential function, because the optimal threshold energy that minimizes the global model-data mismatch for various count rates decreases monotonically with increasing incident count rate.

[0049] The count-rate dependent threshold energy for energy bin b can be modeled by:

[0050]

number

[0051]

number

[0052] C=(c 1 (vector quantity),…, c B Let (vector quantity) be the set of parameters for all bins. The same C was used for all pixels.

[0053] B. Local threshold energy for local mismatch To model the threshold energy for each pixel i, we use a second-order polynomial E local can be added to the global threshold energy. Thus, the threshold energy E thr can be calculated by the following formula:

[0054]

number

[0055]

number

[0056] D i =(d 1,i (vector quantity) , …,d B,i Let (vector quantity) be the parameter set of all bins for pixel i.

[0057] III. Exemplary Procedure for Model Parameter Estimation As mentioned above, the modified cascade PCD output model has seven parameter sets, namely, S 0、 k 0、 H, τ, E thr, C and D. 0 and H can be determined from the specifications of the CT imaging system. The other model parameters can be estimated by a calibration process.

[0058] The PCD data used in the calibration process can be acquired with different thicknesses of ground material at multiple x-ray tube currents. For example, the PCD can be placed approximately 1 m away from the x-ray tube, the tube voltage can be set to 120 kV, and the tube current can be set to 10, 25, 50, 100, 200, and 400 mA. For each data set, 1,200 projections acquired over 1 second can be averaged to reduce the effects of noise. Thus, Δt in equation (5) is 1 / 1200 seconds.

[0059] A total of 30 data sets can be acquired with combinations of air, water, and aluminum slabs of different thicknesses. This includes five blank scan data sets at (25, 50, 100, 200, and 400 mA), three data sets at 50 mA with water at (1, 6, and 16 cm), and eleven different thickness combinations at either 10 mA or 50 mA, respectively. The eleven combinations of water thickness and aluminum thickness (cm, cm) can be (1, 0), (2, 0), (4, 0), (6, 0), (9, 0), (9, 0.5), (12, 0), (12, 0.5), (16, 0), (16, 0.5), and (16, 1). The effective x-ray energy range can be [57.6, 74.4] keV.

[0060] Figure 4A shows a scatter plot of the 30 data points used for model parameter estimation (26 data points) and validation (4 data points) plotted across water thickness, aluminum thickness, and tube current values. In Figure 4B, the initial 120 kVp spectrum and the most attenuated spectrum of the data are shown along with the effective x-ray energy. These 30 data sets can provide a sufficiently wide range of count rates and attenuated spectra.

[0061] Model output and measured data b,i m Attempting to estimate the global and local model parameters (i.e., the threshold energy) by minimizing the error in (a) is computationally expensive, since the model output needs to be calculated for every pixel of every data at every optimization step. To make the calibration process computationally more efficient, a surrogate strategy can be adopted.

[0062] First, the optimal threshold energy of the PCD output model that maximizes the match with the measured energy bin output (i.e., photon counts) can be determined for each bin, each pixel, and each data set. Then, using a function that depends on the count rate versus the threshold energy, the parameters of the function can be estimated by maximizing the match of the threshold energy.

[0063] In one embodiment of the present application, the calibration process can include four steps, which are described below: Note that the term "trimmed pixel" in this application refers to pixels that are within 3 standard deviations from the average count across all data sets.

[0064] Step 1(k 0 , τ, and E thr (0) ): Three model parameters, k 0 , τ, and the minimum threshold energy E thr (0) is the PCD output model y b and the mean y of the cropped pixels (bar symbols) b m It can be estimated by minimizing the difference between the sum of squares of the total counts of

[0065]

number

[0066] Figure 5A shows the measured count rates and the count rates from the modified cascade PCD model using the model parameters obtained in step 1. Each measured count rate and its corresponding error bar are the average sum of all bin counts over T and the standard deviation at each scan condition, respectively.

[0067] Step 2 (E´ thr,b,i ):=(E´ thr,l,i´ ,…,E´ thr,B,i ) be the vector of threshold energies for the B energy bins of pixel i. thr,B,i can be calculated by the following formula:

[0068]

number

[0069] where E´ * thr,i (a) is jointly optimized and unique.

[0070] Step 3 (Global C): Set c of parameters in Eq. (10) b is the global threshold energy E glob (a,c b ) and the average of the optimal threshold energy over the pixels.

[0071]

number

[0072] Figure 5B shows the global threshold function obtained in step 3, E glob (a,c b ) are shown. Each of the marks and the corresponding error bars represent the mean of the optimal energy threshold for the bth bin and the standard deviation of over T, respectively.

[0073] Step 4 (Local D i): The pixel-specific deviation from the average of the cropped pixels is ΔE thr,b,i =E(bar symbol)´ * thr,b (a)-E´ * thr,b Then, the parameter D in Eq. (13) can be calculated as follows: i is optimized for each detector pixel i by

[0074]

number

[0075] The performance of three models can be compared: (a) a PCD output model with default threshold energy and other estimated model parameters (hereafter referred to as the “default model”), (b) a PCD model with the threshold energy globally optimized using Eq. (10) (hereafter referred to as the “global model”), and (c) a PCD model with the threshold energy globally and locally optimized using Eq. (12) (hereafter referred to as the “local model”).

[0076] Figure 6 shows the measured PCD data and the outputs of the three PCD models for the lowest count rate condition of the 10 mA, 16 cm water, and 0.5 cm aluminum test data. The display window for each bin shows the [μ b -2.5σ b ,μ b +2.5σ b ], where μ b and σ b are the mean and standard deviation of the corresponding bin measurements on the pixels, respectively. The same display window width / level, centered on the mean of the measured PCD data for each bin, can be used for all data (i.e., medium grey indicates the mean value).

[0077] The measured PCD data (right-most column) shows large pixel-to-pixel variations, with a fairly consistent pattern among the six bins. The default model values ​​(left-most column) deviate from the average of the measured data, with bins 1-2 and 6 deviating more (light grey) and bin 4 deviating less (darker). Bins 3 and 5 look fine.

[0078] The output of the global model (second from the left) is in good agreement with the average PCD measurements, however, as can be seen by the uniform color, the output of individual pixels is not modeled.

[0079] In contrast, the local model closely matches the measured PCD data for each pixel, for each bin, despite the large pixel-to-pixel variation in the measurements.

[0080] Figure 7 shows the measured PCD data and the output of the three PCD models at the highest count rate condition with a blank scan of 100 mA, where the probability of an event being recorded is 0.51. The display window for each bin is [μ b -2.5σ b ,μ b +2.5σ b ], where μ b and σ b are the mean and standard deviation of the corresponding bin measurements on the pixel, respectively.

[0081] As can be seen in Figure 7, the measured PCD data shows greater pixel-to-pixel variation, with a less consistent pattern across the six bins than in Figure 6. The default model has high values ​​in bins 1-2 and low values ​​in bin 6. The global model has very good agreement with the average value of the measured data in all six bins. The local model has excellent agreement with the measured PCD data at all pixels and in all bins. The pixel-to-pixel variation can be correctly captured by the local model.

[0082] The fit of the model to the data can be assessed in terms of the PCD output (counts) using the MAPE, which can be calculated for each bin independently or for all bins, respectively, by:

[0083]

number

[0084]

number

[0085] where n(T) is the number of cropped pixels. The standard error of MAPE can be calculated by using bootstrap as follows: Bootstrap resampling can be performed 1,000 times, and the above process can be performed for each resampled data to generate 1,000 MAPE values. The standard error of MAPE represents the standard deviation in the 1000 MAPE values. The coefficient of variation (CV) of the count can also be calculated for each bin measurement, as CV allows for relative comparison of bin measurements with respect to pixel-to-pixel variation.

[0086] 8A-8D show the MAPE of the three models calculated for each bin, each of the four test data (left axis), and the CV of the measured data (dashed line, right axis).

[0087] For all test data, the default model shows good agreement (i.e. MAPE of 5-10%) in bins 3-5 (i.e. 45-80 keV range), but significant model-data mismatch (MAPE > 30%) in bins 1-2 (20-45 keV). The MAPE of the global model in bins 1-2 and 6 is significantly lower than the default model. However, it is still large in bin 1, in the range of 25-35%, which may be due to the significant pixel-to-pixel variation indicated by the CV calculated for the measured data. There appears to be a high correlation between the MAPE of the global model and the CV of the measured data. The MAPE of the local models is less than 5% for all test data and less than 2% for most datasets.

[0088] Figure 9 shows the MAPE of the three PCD models, calculated with respect to the incident count rate for the entire test data and plotted against a. The three models have consistent error rates that are nearly independent of the incident count rate. The MAPEs are 44.1–45.2% for the default model, 8.0–9.8% for the global model, and 1.1–2.4% for the local model.

[0089] From the comparison shown in Figures 6-9, it is clear that the global model is effective for global model-data mismatch, and the local model is effective for resolving pixel-to-pixel variations. For the local model, the MAPE of each bin is less than 5% for all test data, and the MAPE averaged over all bins is 1.1-2.4%. Therefore, the developed PCD output model can address both global model-data mismatch and local model-data mismatch, i.e., pixel-to-pixel variations. Furthermore, the MAPE of the three models is consistent for different incident count rates and x-ray beam filtration. This indicates that the performance of the developed PCD model is robust to the changes in the x-ray spectrum as well as the changes in the incident count rate, since the four test data were acquired with different material thicknesses.

[0090] Those skilled in the art can envision various potential applications of the developed PCD method in CT imaging. One such application can be a simulator for estimating PCD output data under specific conditions in CT imaging. A user of the simulator can input various imaging parameters, including but not limited to X-ray tube settings, PCT settings, imaging material thickness, etc., to obtain simulated PCD output. The salient interpretations of each fundamental detection mechanism provided by the developed PCD model will be of great help in creating such a PCD simulator.

[0091] Another exemplary application is the development of correction or compensation methods to mitigate the effects of charge sharing and pulse pile-up in CT imaging. The developed PCT model can be incorporated, for example, into the material decomposition or reconstruction algorithms of a CT imaging system.

[0092] By integrating this application method with the data processing pipeline of a CT system, the developed PCD output model can assist in generating output data without spectral distortion. Thus, the effects due to charge sharing and pulse pile-up in the PCD output data (or reconstructed image) can be corrected or compensated for. This approach leads to improved image quality, enhanced contrast resolution, and reduced noise. The efficient parameter estimation and accuracy of this model also bring practical benefits to algorithms based on this model.

[0093] The model determination, correction and / or compensation algorithms can be implemented in a photon-counting CT scanner system, as described below with reference to Fig. 10. The X-ray CT apparatus 1 shown in Fig. 10 includes a gantry 10, a bed 30, and a console 40 for executing processing of the medical imaging processing apparatus. For convenience of explanation, Fig. 10 shows a plurality of gantry 10.

[0094] In this embodiment, the rotation axis of the rotating frame 13 in the non-inclined state, i.e., the longitudinal direction of the top plate 33 of the bed 30, is defined as the "Z-axis direction," the axis direction perpendicular to the Z-axis direction and horizontal to the floor surface is defined as the "X-axis direction," and the axis direction perpendicular to the Z-axis direction and perpendicular to the floor surface is defined as the "Y-axis direction."

[0095] For example, the gantry 10 and the bed 30 are installed in a CT examination room, and the console 40 is installed in a control room adjacent to the CT examination room. The console 40 is not necessarily installed in the control room. For example, the console 40 can be installed in the same room as the gantry 10 and the bed 30. In any case, the gantry 10, the bed 30, and the console 40 are connected to each other so as to be able to communicate with each other via wires or wirelessly.

[0096] The gantry 10 is a scanner having a configuration for performing X-ray CT imaging on a subject (or an imaging target) P. The gantry 10 includes an X-ray tube 11, an X-ray detector 12, a rotating frame 13, an X-ray high voltage device 14, a control device 15, a wedge filter 16, a collimator 17, and a data acquisition system (DAS) 18.

[0097] The X-ray tube 11 is a vacuum tube that generates X-rays by emitting thermoelectrons from a cathode (filament) to an anode (target) in response to application of a high voltage and supply of a filament current from the X-ray high voltage device 14. Specifically, X-rays are generated when the thermoelectrons collide with the target. An example of the X-ray tube 11 is a rotating anode type X-ray tube that generates X-rays by emitting thermoelectrons from a rotating anode. The X-rays generated by the X-ray tube 11 are shaped into a cone beam by, for example, a collimator 17, and applied to the subject P.

[0098] The X-ray detector 12 detects X-rays irradiated by the X-ray tube 11 and transmitted through the subject P, and outputs an electrical signal according to the X-ray dose to the DAS 18. The X-ray detector 12 includes, for example, a plurality of X-ray detection element rows, each including a plurality of X-ray detection elements aligned in the channel direction (X-axis direction, i.e., row direction) along an arc centered on the focal point of the X-ray tube 11. The X-ray detector 12 has an array structure in which a plurality of X-ray detection element rows, each including a plurality of X-ray detection elements aligned in the channel direction, are aligned in the slice direction (Z-axis direction, i.e., row direction).

[0099] Specifically, the X-ray detector 12 may be, for example, a direct conversion detector including a semiconductor element that converts incident X-rays into an electrical signal. The X-ray detector 12 is an example of a PCD according to this embodiment and is also referred to as a "PCD 12."

[0100] The rotating frame 13 supports the X-ray generator and the X-ray detector 12 rotatably around a rotation axis. Specifically, the rotating frame 13 is an annular frame that supports the X-ray tube 11 and the X-ray detector 12 so that the X-ray tube 11 faces the X-ray detector 12, and rotates the X-ray tube 11 and the X-ray detector 12 under the control of a control device 15 described later. The rotating frame 13 is rotatably supported by a fixed frame (not shown) made of a metal such as aluminum. Specifically, the rotating frame 13 is connected to an end of the fixed frame via a bearing. The rotating frame 13 rotates at a predetermined angular velocity around the rotation axis Z while receiving power from a driver of the control device 15.

[0101] In addition to the X-ray tube 11 and the X-ray detector 12, the rotating frame 13 includes and supports an X-ray high voltage device 14 and a DAS 18. Such a rotating frame 13 is housed in a substantially cylindrical housing having a bore 19 that defines an imaging space. The bore approximately coincides with the FOV. The central axis of the bore corresponds to the rotation axis Z of the rotating frame 13. Detection data generated by the DAS 18 is transmitted, for example, from a transmitter (not shown) disposed in a non-rotating part of the frame (such as a fixed frame, not shown in FIG. 10) to a receiver (not shown) and transferred to the console 40.

[0102] X-ray high voltage device 14 includes a high voltage generator including electric circuits such as a transformer and a rectifier, and having a function of generating a high voltage to be applied to X-ray tube 11 and a filament current to be supplied to X-ray tube 11, and an X-ray control device configured to control the output voltage according to the X-rays irradiated by X-ray tube 11. The high voltage generator may be of a transformer type or an inverter type. X-ray high voltage device 14 may be provided on rotating frame 13, which will be described later, or on a fixed frame (not shown) of gantry 10.

[0103] The control device 15 includes a processing circuit including a CPU (Central Processing Unit) and the like, and a driver for a motor or a drive device. The processing circuit includes, as hardware resources, a processor such as a CPU or an MPU (Micro Processing Unit) and a memory such as a Read Only Memory (ROM) or a Random Access Memory (RAM). The control device 15 can be realized by an Application Specific Integrated Circuit (ASIC), a Field Programmable Gate Array (FPGA), or other Complex Programmable Logic Device (CPLD) or Simple Programmable Logic Device (SPLD). The control device 15 controls the X-ray high voltage device 14, the DAS 18, and the like according to instructions from the console 40. The processor performs the above control by reading and executing a program stored in the memory.

[0104] The CPU may execute a computer program including a set of computer readable instructions to perform the functions described herein, the program being stored in any of the non-transitory electronic memories and / or hard disk drives, CDs, DVDs, flash drives, or other known storage media as described above. Additionally, the computer readable instructions may be provided as a utility application, background daemon, or operating system component, or combination thereof, and executed in conjunction with a processor and operating system as known to those skilled in the art. Additionally, the CPU may execute as multiple processors operating cooperatively in parallel to execute instructions.

[0105] The control device 15 also has a function of controlling the operation of the gantry 10 and the bed 30 in response to an input signal from an input interface 43 (described later) attached to the console 40 or the gantry 10. For example, the control device 15 controls the rotation of the rotating frame 13, the tilt of the gantry 10, or the operation of the bed 30 and the tabletop 33 in response to the input signal. The control of tilting the gantry 10 is executed by the control device 15 rotating the rotating frame 13 around an axis parallel to the X-axis direction based on tilt angle information input via the input interface 43 attached to the gantry 10. The control device 15 can be provided in either the gantry 10 or the console 40. The control device 15 can be configured by directly incorporating a program into the circuit of the processor, rather than storing the program in a memory. In this case, the processor executes the above-mentioned control by reading and executing the program incorporated in the circuit.

[0106] The wedge filter 16 is a filter for adjusting the dose of X-rays irradiated from the X-ray tube 11. Specifically, the wedge filter 16 is a filter that transmits the X-rays irradiated from the X-ray tube 11 and attenuates the X-rays so that the X-rays irradiated from the X-ray tube 11 to the subject P show a predetermined distribution. For example, the wedge filter 16 (or a bowtie filter) is a filter obtained by processing aluminum to have a predetermined target angle and a predetermined thickness.

[0107] The collimator 17 is a lead plate or the like for narrowing the application range of the X-rays transmitted through the wedge filter 16, and includes a slit formed by combining lead plates or the like. The collimator 17 is sometimes called an "X-ray aperture."

[0108] The DAS 18 generates digital data (also called "detection data") indicating the count of X-rays detected by the X-ray detector 12 for each of a plurality of energy bands (also called "energy bins" or simply "bins"). The detection data is a set of count value data identified by the channel number and row number of the X-ray detection element that generated the detection data, the view number indicating the collected view (also called the projection angle), and the energy bin number. The DAS 18 is realized, for example, by an application specific integrated circuit (ASIC) that implements circuit elements capable of generating the detection data. The detection data is transferred to the console 40.

[0109] The bed 30 is a device for moving the subject P while placing the subject P thereon for scanning, and includes a base 31, a bed driving device 32, a top plate 33, and a support frame .

[0110] The base 31 is a housing that supports the support frame 34 so that the support frame 34 is movable in the vertical direction.

[0111] The bed driving device 32 is a motor or a driving device that moves the tabletop 33 on which the subject P is placed in the longitudinal direction of the tabletop 33. The bed driving device 32 moves the tabletop 33 under the control of the console 40 or the control of the control device 15. For example, the bed driving device 32 moves the tabletop 33 in a direction perpendicular to the subject P so that the body axis of the subject P placed on the tabletop 33 coincides with the central axis of the bore of the rotating frame 13. The bed driving device 32 can also move the tabletop 33 in the body axis direction of the subject P in accordance with X-ray CT imaging performed using the gantry 10. The bed driving device 32 generates electricity by driving at a rotation speed according to the duty ratio of a drive signal from the control device 15. The bed driving device 32 is realized by a motor such as a direct drive motor or a servo motor.

[0112] The tabletop 33 provided on the upper surface of the support frame 34 is a plate on which the subject P is placed. The bed driving device 32 can move not only the tabletop 33 but also the support frame 34 in the longitudinal direction of the tabletop 33.

[0113] The console 40 includes a memory 41, a display 42, an input interface 43, and a processing circuit 44. Data communication between the memory 41, the display 42, the input interface 43, and the processing circuit 44 is performed via a bus. Although the console 40 is described as being separate from the gantry 10, the gantry 10 may include the console 40 or may include some of the components of the console 40.

[0114] The memory 41 is a storage device such as a hard disk drive (HDD), a solid state drive (SSD), or an integrated circuit storage device, and stores various types of information. The memory 41 stores, for example, projection data and reconstructed image data. The memory 41 is not limited to an HDD, an SSD, or the like, and may be, for example, a portable storage medium such as a CD, a DVD, or a flash memory, or a driver for reading and writing various types of information between the memory 41 and a semiconductor memory such as a random access memory (RAM). The storage area of ​​the memory 41 may be provided in the X-ray CT device 1, or may be provided in an external storage device connected via a network. For example, data of a CT image or a display image is stored in the memory 41. In addition, the memory 41 stores a control program according to this embodiment.

[0115] The display 42 displays various information. For example, the display 42 outputs medical images (CT images) generated by the processing circuit 44 and a GUI (Graphical User Interface) for receiving various operations from an operator. As the display 42, for example, a liquid crystal display (LCD), a cathode ray tube (CRT) display, an organic electro luminescence display (OELD), a plasma display, or any other display can be appropriately used. The display 42 may be provided on the stand 10. The display 42 may be a desktop type, or may be configured by a tablet terminal capable of wireless communication with the console 40.

[0116] The input interface 43 receives various input operations from an operator, converts the received input operations into electrical signals, and outputs the electrical signals to the processing circuitry 44. For example, the input interface 43 receives from the operator collection conditions for collecting projection data, reconstruction conditions for reconstructing a CT image, image processing conditions for generating a post-processed image from a CT image, and the like. As the input interface 43, for example, a mouse, a keyboard, a trackball, a switch, a button, a joystick, a touchpad, or a touch panel display can be appropriately used. In this embodiment, the input interface 43 does not necessarily include physical operation parts such as a mouse, a keyboard, a trackball, a switch, a button, a joystick, a touchpad, or a touch panel display. For example, the input interface 43 also includes an electrical signal processing circuit that receives an electrical signal corresponding to an input operation from an external input device provided separately from the device and outputs the electrical signal to the processing circuitry 44. The input interface 43 may be provided on the pedestal 10. The input interface 43 may be configured by a tablet terminal capable of wireless communication with the console 40.

[0117] The processing circuit 44 controls the overall operation of the X-ray CT device 1 in response to an electrical signal of an input operation output from the input interface 43. For example, the processing circuit 44 includes a processor such as a CPU, an MPU, or a graphics processing unit (GPU), and a memory such as a ROM or a RAM as hardware resources. The processing circuit 44 executes a system control function 441, a pre-processing function 442, a reconstruction function 443, and a display control function 444 by the processor executing a program loaded in the memory. Each of the functions (the system control function 441, the pre-processing function 442, the reconstruction function 443, and the display control function 444) is not necessarily realized by a single processing circuit. A processing circuit can be configured by combining multiple independent processors, and the processors can execute the respective programs to realize the functions.

[0118] The system control function 441 controls each function of the processing circuit 44 based on an input operation received from an operator via the input interface 43. Specifically, the system control function 441 reads out a control program stored in the memory 41, loads it into the memory in the processing circuit 44, and controls each part of the X-ray CT device 1 according to the loaded control program. For example, the processing circuit 44 executes each function of the processing circuit 44 based on an input operation received from an operator via the input interface 43. For example, the system control function 441 acquires a two-dimensional positioning image of the subject P and determines a scan range, imaging conditions, and the like. The positioning image may also be called a "scanogram" or a "scout image."

[0119] The pre-processing function 442 generates data obtained by performing pre-processing on the detection data output from the DAS 18, such as logarithmic conversion processing, offset correction processing, inter-channel sensitivity correction processing, beam hardening correction, as well as correction for detector calibration, detector nonlinearity, polarity effect, noise balance, and material decomposition. The data before pre-processing (detection data) and the data after pre-processing are sometimes collectively referred to as "projection data." The pre-processing function 442 is an example of a pre-processor.

[0120] The reconstruction function 443 generates CT image data by performing reconstruction processing using a filtered backprojection method, an iterative reconstruction method, a stochastic image reconstruction method, or the like on the projection data generated by the preprocessing function 442. The reconstruction function 443 is an example of a reconstruction processor. Image filtering, smoothing, volume rendering, or image difference processing can be applied to the CT image data as necessary. The display control function 444 converts the CT image data generated by the reconstruction function 443 into tomographic image data of a predetermined cross section, that is, three-dimensional image data by a known method, based on an input operation received from an operator via the input interface 43. The generation of three-dimensional image data can be performed directly by the reconstruction function 443. The display control function 444 is an example of a display control device.

[0121] In one embodiment, the X-ray tube 11 is a single source that emits a wide spectrum of X-ray energies, and the PCD 12 can use direct X-ray radiation detectors based on semiconductors such as cadmium telluride (CdTe), cadmium zinc telluride (CZT), silicon (Si), mercury iodide (HgI2), and gallium arsenide (GaAs). As mentioned above, semiconductor-based direct X-ray detectors generally have a much faster time response than indirect detectors such as scintillator detectors. The fast time response of direct detectors allows for the resolution of individual X-ray detection events, but some pile-up of detection events may occur at high X-ray fluxes typical of clinical X-ray applications. The energy of the detected X-rays is proportional to the signal generated by the direct detector, and the detection events can be organized into energy bins to obtain spectrally resolved X-ray data for spectral CT.

[0122] Numerous modifications and variations of the embodiments presented herein are possible in light of the above teachings. It is therefore to be understood that, within the scope of the appended claims, the application may be practiced otherwise than as specifically described herein. The invention is not limited to the examples just described. In particular, features of the illustrated examples may be combined with one another in variations not shown.

[0123] The embodiments of the present disclosure may also be as described in the following appendices.

[0124] (1) A method for determining a model characterizing an output from a photon counting detector (PCD) used in a computed tomography (CT) system, the PCD having a plurality of pixels, the method including: constructing a PCD output model having a plurality of model parameters including a first model parameter set, the first model parameter set being dependent on an incident count rate on the PCD and dependent on a pixel position within the PCD; receiving calibration data acquired by scanning a plurality of basis material combinations under a plurality of incident count rates; and estimating the plurality of model parameters based on the received calibration data.

[0125] (2) The method of (1), wherein the first model parameter set includes a first sub-parameter set dependent on an incident count rate and a second sub-parameter set dependent on a pixel position within the PCD, and the estimating step further includes estimating initial values ​​of the plurality of model parameters such that a total count error between an output derived from the PCD output model and the received calibration data is minimized, determining the first sub-parameter set such that a global model-to-data mismatch across a plurality of pixels is minimized, and determining the second sub-parameter set such that pixel-to-pixel variation is minimized.

[0126] (3) The method of (1), wherein the first set of model parameters is one of a detector dead time set of the PCD, a charge sharing matrix set of the PCD, and a threshold energy vector set of the PCD.

[0127] (4) The method of (1), wherein the constructing step further includes a step of determining, as the constructed PCD output model, a cascade model having sub-models that respectively characterize material damping effects, charge sharing effects, pulse pile-up effects, and energy binning operations.

[0128] (5) The method of (1), further comprising the steps of receiving validation data acquired by scanning a combination of a plurality of basis materials under a plurality of incident count rates, and evaluating performance of a PCD output model having a plurality of estimated model parameters based on the received validation data.

[0129] (6) The method of (1), further comprising the steps of receiving a number of parameters specifying operating conditions of the PCD, and generating a simulation output of the PCD using a PCD output model having a number of estimated model parameters based on the received number of parameters.

[0130] (7) The method of (1), further comprising the steps of receiving scan data acquired by scanning an imaging object using a CT system, correcting the received scan data or compensating for effects of spectral distortion contained in the received scan data based on a PCD output model having a plurality of estimated model parameters, and reconstructing an image of the imaging object based on the corrected scan data.

[0131] (8) An apparatus for determining a model characterizing an output from a photon counting detector (PCD) used in a computed tomography (CT) system, the PCD having a plurality of pixels, the apparatus comprising: a processing circuit configured to: construct a PCD output model having a plurality of model parameters including a first model parameter set, the first model parameter set being dependent on an incident count rate on the PCD and dependent on a pixel position within the PCD; receive calibration data obtained by scanning a plurality of basis material combinations under a plurality of incident count rates; and estimate the plurality of model parameters based on the received calibration data.

[0132] (9) The apparatus of (8), wherein the first model parameter set includes a first sub-parameter set dependent on an incident count rate and a second sub-parameter set dependent on a pixel position within the PCD, and the processing circuitry is configured to estimate initial values ​​of the model parameters such that a total count error between an output derived from the PCD output model and the received calibration data is minimized, determine the first sub-parameter set such that a global model to data mismatch across multiple pixels is minimized, and determine the second sub-parameter set such that pixel-to-pixel variation is minimized.

[0133] (10) The apparatus described in (8), wherein the first set of model parameters is one of a detector dead time set for the PCD, a charge sharing matrix set for the PCD, and a threshold energy vector set for the PCD.

[0134] (11) The apparatus of (8), wherein the processing circuitry is configured to determine, as the constructed PCD output model, a cascade model having sub-models that respectively characterize material attenuation effects, charge sharing effects, pulse pile-up effects, and energy binning operations.

[0135] (12) The apparatus of (8), wherein the processing circuitry is configured to receive validation data acquired by scanning a combination of a plurality of basis materials under a plurality of incident count rates, and to evaluate performance of a PCD output model having a plurality of estimated model parameters based on the received validation data.

[0136] (13) The apparatus described in (8), wherein the processing circuitry is configured to receive a number of parameters specifying operating conditions of the PCD and generate a simulation output of the PCD using a PCD output model having a number of estimated model parameters based on the received number of parameters.

[0137] (14) The apparatus described in (8), wherein the processing circuit is configured to receive scan data acquired by scanning an imaging object using a CT system, correct the received scan data or compensate for effects of spectral distortion contained in the received scan data based on a PCD output model having a plurality of estimated model parameters, and reconstruct an image of the imaging object based on the corrected scan data.

[0138] (15) A non-transitory computer-readable medium having stored thereon a program that, when executed by a processing circuit, causes the processing circuit to perform a method for determining a model characterizing an output from a photon counting detector (PCD) used in a computed tomography (CT) system, the PCD having a plurality of pixels, the method including the steps of constructing a PCD output model having a plurality of model parameters including a first model parameter set, the first model parameter set being dependent on an incident count rate on the PCD and dependent on a pixel position within the PCD; receiving calibration data obtained by scanning a plurality of basis material combinations under a plurality of incident count rates; and estimating the plurality of model parameters based on the received calibration data.

[0139] (16) The non-transitory computer-readable medium of (15), wherein the first model parameter set includes a first sub-parameter set dependent on an incident count rate and a second sub-parameter set dependent on a pixel position within the PCD, and the estimating step further includes estimating initial values ​​of the plurality of model parameters such that a total count error between an output derived from the PCD output model and the received calibration data is minimized, determining the first sub-parameter set such that a global model-to-data mismatch across a plurality of pixels is minimized, and determining the second sub-parameter set such that pixel-to-pixel variation is minimized.

[0140] (17) The non-transitory computer-readable medium of (15), wherein the first set of model parameters is one of a detector dead time set for the PCD, a charge sharing matrix set for the PCD, and a threshold energy vector set for the PCD.

[0141] (18) The non-transitory computer-readable medium of (15), wherein the constructing step further includes determining, as the constructed PCD output model, a cascade model having sub-models that respectively characterize material damping effects, charge sharing effects, pulse pile-up effects, and energy binning operations.

[0142] (19) The non-transitory computer-readable medium of (15), wherein the method further includes receiving a number of parameters specifying operating conditions of the PCD, and generating a simulation output of the PCD using a PCD output model having a plurality of estimated model parameters based on the received number of parameters.

[0143] (20) The non-transitory computer-readable medium of (15), wherein the method further includes the steps of receiving scan data acquired by scanning an imaging object using a CT system, correcting the received scan data or compensating for effects of spectral distortion contained in the received scan data based on a PCD output model having a plurality of estimated model parameters, and reconstructing an image of the imaging object based on the corrected scan data.

[0144] Numerous modifications and variations of the embodiments presented herein are possible in light of the above teachings, and it is therefore to be understood that, within the scope of the appended claims, the present disclosure may be practiced otherwise than as specifically described herein.

Claims

1. 1. A method for determining a model characterizing an output from a Photon-Counting Detector (PCD) for use in a Computed Tomography (CT) system, the PCD having a plurality of pixels, the method comprising: constructing a PCD output model having a plurality of model parameters including a first model parameter set, the first model parameter set being dependent on an incident count rate on the PCD and dependent on a pixel position within the PCD; receiving calibration data acquired by scanning a plurality of basis material combinations under a plurality of incident count rates; estimating the plurality of model parameters based on the received calibration data; The method includes:

2. the first model parameter set includes a first sub-parameter set dependent on the incident count rate and a second sub-parameter set dependent on the pixel location within the PCD, and the estimating step comprises: estimating initial values ​​of the model parameters such that a total error between an output derived from the PCD output model and the received calibration data is minimized; determining the first sub-parameter set such that a global model and data mismatch across the plurality of pixels is minimized; determining said second sub-parameter set such that pixel-to-pixel variation is minimized; The method of claim 1 further comprising:

3. The first set of model parameters: A detector dead time set for said PCD; a set of charge-sharing matrices for the PCD; and A set of threshold energy vectors for the PCD The method of claim 1 , wherein the first and second electrodes are one of:

4. The constructing step further comprises: determining a cascade model having sub-models that respectively characterize the attenuation effect, the charge sharing effect, the pulse pile-up effect, and the energy binning behavior of the material as the constructed PCD output model; The method of claim 1 further comprising:

5. receiving validation data acquired by scanning the plurality of basis material combinations under the plurality of incidence count rates; evaluating performance of the PCD output model having the estimated model parameters based on the received validation data; The method of claim 1 further comprising:

6. receiving a number of parameters specifying operating conditions of the PCD; generating a simulation output of the PCD using the PCD output model having the estimated model parameters based on the received number of parameters; The method of claim 1 further comprising:

7. receiving scan data acquired by scanning an imaging object using the CT system; correcting the received scan data or compensating for effects of spectral distortions contained in the received scan data based on the PCD output model having the estimated model parameters; reconstructing an image of the imaging subject based on the corrected scan data. The method of claim 1 further comprising:

8. 1. An apparatus for determining a model characterizing an output from a Photon-Counting Detector (PCD) for use in a Computed Tomography (CT) system, the PCD having a plurality of pixels, the apparatus comprising: constructing a PCD output model having a plurality of model parameters including a first model parameter set, the first model parameter set being dependent on an incident count rate on the PCD and dependent on pixel position within the PCD; receiving calibration data obtained by scanning a plurality of basis material combinations under a plurality of incident count rates; Estimating the plurality of model parameters based on the received calibration data. A processing circuit configured as follows: An apparatus comprising:

9. the first model parameter set includes a first sub-parameter set dependent on the incident count rate and a second sub-parameter set dependent on the pixel location within the PCD, and the processing circuitry: estimating initial values ​​of the model parameters such that a total error between the output derived from the PCD output model and the received calibration data is minimized; determining the first sub-parameter set such that a global model and data mismatch across the plurality of pixels is minimized; determining said second sub-parameter set such that pixel-to-pixel variation is minimized; The apparatus of claim 8 , configured as follows:

10. The first set of model parameters: A detector dead time set for said PCD; a set of charge-sharing matrices for the PCD; and A set of threshold energy vectors for the PCD The apparatus of claim 8, wherein the

11. The processing circuitry comprises: As the constructed PCD output model, a cascade model is determined having sub-models that respectively characterize the material's attenuation effect, charge sharing effect, pulse pile-up effect, and energy binning operation. The apparatus of claim 8 , configured as follows:

12. The processing circuitry comprises: receiving validation data acquired by scanning the plurality of basis material combinations under the plurality of incident count rates; Evaluating performance of the PCD output model having the estimated model parameters based on the received validation data. The apparatus of claim 8 , configured as follows:

13. The processing circuitry comprises: receiving a number of parameters specifying operating conditions of said PCD; generating a simulation output of the PCD using the PCD output model having the estimated model parameters based on the received number of parameters; The apparatus of claim 8 , configured as follows:

14. The processing circuitry comprises: receiving scan data acquired by scanning an imaging object using the CT system; correcting the received scan data or compensating for effects of spectral distortions contained in the received scan data based on the PCD output model having the estimated model parameters; Reconstructing an image of the imaging object based on the corrected scan data. The apparatus of claim 8 , configured as follows:

15. 1. A non-transitory computer readable medium having stored thereon a program that, when executed by a processing circuit, causes the processing circuit to perform a method for determining a model that characterizes an output from a Photon-Counting Detector (PCD) for use in a Computed Tomography (CT) system, the PCD having a plurality of pixels, the method comprising: constructing a PCD output model having a plurality of model parameters including a first model parameter set, the first model parameter set being dependent on an incident count rate on the PCD and dependent on a pixel position within the PCD; receiving calibration data acquired by scanning a plurality of basis material combinations under a plurality of incident count rates; estimating the plurality of model parameters based on the received calibration data; A non-transitory computer readable medium comprising:

16. the first model parameter set includes a first sub-parameter set dependent on the incident count rate and a second sub-parameter set dependent on the pixel location within the PCD, and the estimating step comprises: estimating initial values ​​of the model parameters such that a total error between the output derived from the PCD output model and the received calibration data is minimized; determining the first sub-parameter set such that a global model and data mismatch across the plurality of pixels is minimized; determining said second sub-parameter set such that pixel-to-pixel variation is minimized; 20. The non-transitory computer-readable medium of claim 15, further comprising:

17. The first set of model parameters: A detector dead time set for said PCD; a set of charge-sharing matrices for the PCD; and A set of threshold energy vectors for the PCD 20. The non-transitory computer readable medium of claim 15, wherein:

18. The constructing step further comprises: determining a cascade model having sub-models that respectively characterize the attenuation effect, the charge sharing effect, the pulse pile-up effect, and the energy binning behavior of the material as the constructed PCD output model; 20. The non-transitory computer-readable medium of claim 15, further comprising:

19. The method further comprising: receiving a number of parameters specifying operating conditions of the PCD; generating a simulation output of the PCD using the PCD output model having the estimated model parameters based on the received number of parameters; 20. The non-transitory computer-readable medium of claim 15, further comprising:

20. The method further comprising: receiving scan data acquired by scanning an imaging object using the CT system; correcting the received scan data or compensating for effects of spectral distortions contained in the received scan data based on the PCD output model having the estimated model parameters; reconstructing an image of the imaging subject based on the corrected scan data.

20. The non-transitory computer-readable medium of claim 15, further comprising:

Images