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Recently developed x-ray transmittance modeling-based three-step algorithm compensates for the spectral distortion in the photon-counting detector (PCD) and estimates the line-integrals of the basis materials. The x-ray transmittance modeling linearizes the nonlinear forward imaging model and derives a computationally efficient three-step algorithm that achieves almost unbiased and minimum variance estimator. In this article, we apply the algorithm to the experimental data from a research whole-body PCD-computed tomography (CT) system. We perform pixel-by-pixel calibration using water-equivalent phantoms to fit the output of the scanner to the forward model and then feed the calibrated data into the three-step algorithm. Experimental data from iodine phantom and swine abdomen scans demonstrate that the proposed algorithm compensates for the spectral distortion effectively and estimates the line-integrals of two basis materials, water and iodine, efficiently. The proposed method substantially reduces the beam hardening and ring artifacts present in the test phantom compared to those of the image-based material decomposition method and the images directly reconstructed from the raw data of the system. The algorithm also exhibits less bias and comparable noise to those of the other methods for various x-ray energies.

PURPOSE: Spectral distortion due to charge sharing (CS) and pulse pileup (PP) in photon counting detectors (PCDs) degrades the quality of PCD data. We recently proposed multi-energy inter-pixel coincidence counters (MEICC) that provided spectral cross-talk information related to CS. When PP was absent, the normalized Cramér–Rao lower bounds (nCRLBs) of 225-μm pixel PCDs with MEICC was comparable to those of 450-μm pixel PCD without MEICC. The aim of this study was to assess the performance of PCDs with MEICC at the presence of both CS and PP using computer simulations. METHODS: An in-house Monte Carlo program was modified to incorporate the following four temporal elements: (1) A pulse shape with a pulse duration of 20 ns, (2) delays of up to 10 ns in anode arrival times when photons were incident on pixel boundaries, (3) offsets proportional to a vertical separation between the primary and secondary charge clouds at the rate of ±4 ns per ±100 μm, and (4) a stochastic fluctuation of anode arrival times for all of the charge clouds with a standard deviation of 2 ns. We assessed the performance of five PCDs, (a)–(f), for three spectral tasks, (A)–(C): (a) The conventional PCD, (b) a PCD with MEICC, (c) a PCD with one coincidence counter (1CC), (d) a PCD with a 3×3 analog charge summing scheme (ACS), and (e) a PCD with a 3×3 digital count summing scheme (DCS); (A) conventional CT imaging with water (i.e., linear attenuation coefficient maps), (B) water–bone material decomposition, and (C) K-edge imaging with tungsten. The tube current was changed from 1 mA to 1,000 mA and the nCRLB was assessed. RESULTS: The recorded count rate curves were fitted by the non-paralyzable detection model with the effective deadtime parameter. The best fit was achieved by 25.8 ns for the conventional PCD, 18.6 ns for MEICC and 1CC, 140.5 ns for ACS, and 209.0 ns for DCS. The nCRLBs were strongly dependent on count rates. MEICC provided the best nCRLBs for all of the imaging tasks over the count rate range investigated except for a few conditions such as K-edge imaging at 1 mA. PP decreased the merit of MEICC over the conventional PCD in addressing CS. Nonetheless, MEICC consistently provided better nCRLBs than the conventional PCD did. The nCRLBs of MEICC were in the range of 49–58% of those of the conventional PCD for K-edge imaging, 45–76% for water–bone material decomposition, and 81–88% for the conventional CT imaging (i.e., linear attenuation coefficient maps). ACS provided better nCRLBs than the conventional PCD did only when the effect of PP was minor (e.g., when the counting efficiency of the conventional PCD was higher than 0.95 with the tube current of up to 100 mA). CONCLUSION: Besides a few cases, MEICC provides the best nCRLBs for all of the tasks at all of the count rates. ACS and DCS provides better nCRLBs than the conventional PCD does only when count rates are very low.

Recently, multienergy interpixel coincidence counter (MEICC) has been proposed for charge sharing (CS) correction and compensation for photon counting detectors (PCDs), which uses energy-dependent coincidence counters to record coincident events between multiple energy windows of a pixel-of-interest and those of neighboring pixels. A Monte Carlo (MC) simulation study was performed to assess the performance of MEICC; however, the performance might have been overestimated in a previous study. The CS increases the number of photons recorded at a PCD pixel at the expense of the spatial resolution, and therefore, when spatially uniform flat-field X-ray signals are used, it gives PCDs with CS more signals than a PCD without CS. In this article, we propose to use spatially contained boxcar signals for evaluating the performances for high spatial frequency tasks because they provide consistent signals regardless of the presence or absence of CS. The flat-field signals must be used for low spatial frequency tasks. We assessed the performances of MEICC and other PCDs with both flat-field signals and boxcar signals, with optimal threshold energies, and with two different pixel sizes. As it is expected, normalized Cramer–Rao lower bounds (nCRLBs) measured with the boxcar signals were worse than those with flat-field signals in general. The nCRLBs of MEICC with 225- $\mu \text{m}$ pixel were close to the current 450- $\mu \text{m}$ PCD. We studied a combination of flat-field signals and $N\times N$ super-pixels, where the output of $N\times N$ pixels were added, using an MC simulation and a simple CS counting model. The study showed that CS had two opposing impacts on the conventional computed tomography imaging—a negative impact with double-counting among $N\times N$ pixels and a positive impact with single-counting spill-in and spill-out across the super-pixel boundary—and the positive impact diminished with increasing $N$ . A use of large $N\times N$ super-pixels such as $N\geq 25$ was suggested to approximate the zero-frequency detection quantum efficiency of PCD with CS.

The performance of photon counting detectors (PCDs) are limited by the spectral distortion caused by charge sharing and pulse pileup. Recently we have proposed a new detector design called MEICC for multi-energy inter-pixel coincidence counter. MEICC records the counting signals in the same way as the current PCDs, while also recording the energy-dependent cross-talk with neighboring pixels. The previous studies have shown that MEICC decreases the effect of charge sharing significantly. Building on the previous success, the aim of this study was to assess the performance of MEICC when the pulse pileup also causes spectral distortion (in addition to charge sharing). Monte Carlo simulations have been performed to compare the performance of MEICC, the current PCD, and two different versions of real-time charge sharing correction schemes. The study found that MEICC had the best performance when count rates were moderate or high.

One of the challenges in photon counting detector (PCD)-based computed tomography (CT) is the spectral distortion in the PCD caused by physical effects such as charge sharing and K-escape fluorescence. This chapter summarizes for conventional approaches to compensate for the spectral distortion in PCD-CT and provides in great detail for a recently developed x-ray transmittance modeling-based three-step algorithm as a fast alternative to the maximum likelihood-based estimator. We describe both theoretical and practical aspects of the algorithm and also provide an example of two-material decomposition with practical implementations.

Purpose Smaller pixel sizes of x-ray photon counting detectors (PCDs) are advantageous for count rate capabilities but disadvantageous for charge sharing. With charge sharing, the energy of an x-ray photon may be split and one photon may produce two or more counts at adjacent pixels, both at lower energies than the incident energy. This "double-counting" increases noise variance and degrades the spectral response. Overall, it has a significantly negative impact on the performance of PCD-based computed tomography (CT). Charge sharing is induced by the detection physics and occurs regardless of count rates; thus, it is impossible to avoid. We propose in this paper a method that has a potential to address both noise and bias added by charge sharing. Methods We propose applying a multi-energy inter-pixel coincidence counter (MEICC) technique, which uses energy-dependent coincidence counters, keeps the book of charge sharing events during data acquisition, and provides the exact number of charge sharing occurrences, which can be used to either correct or compensate for them after the acquisition is completed. MEICC does not interfere with the primary counting process; therefore, PCDs with MEICC will remain as fast as those without MEICC. MEICC can be implemented using current electronics technology because its inter-pixel coincidence counters used to handle digital data are rather simple. We evaluated Cramer-Rao lower bound (CRLB) of PCDs with and without MEICC using a Monte Carlo simulation. Results When the number of energy windows was four or larger and eight neighboring pixels were used, the CRLBs of 225-µm PCD with MEICC normalized by those of the current PCD with the same number of windows were 0.361-0.383 for water density images of two basis functions, which was only 5.7-16.4% worse than those of a PCD without charge sharing (which were at 0.329-0.358). In contrast, the normalized CRLBs of the PCD with one coincidence counter were 0.466-0.499, which were 37.3-45.6% worse than the PCD without charge sharing. The use of eight neighboring pixels provided ~10% better CRLB values than four neighboring pixels for MEICC. With four energy windows, decreasing the number of coincidence counters from 16 to 9 only slightly increased the CRLB from 0.255 to 0.269 (which corresponded to as little as a 5.5% change). The normalized CRLBs of MEICC for K-edge imaging (gold) were 0.295-0.426, while those of the one coincidence counter were 0.926-0.959 and the ideal PCDs were 0.126-0.146. Conclusions The proposed MEICC provides spectral information that can be used to address charge sharing problems in PCDs and is expected to satisfy the requirements for clinical x-ray CT. MEICC is very effective, especially for K-edge imaging, which requires accurate spectral information.

Recently, multi-energy inter-pixel coincidence counter (MEICC) has been proposed for charge sharing correction and compensation for photon counting detectors (PCDs), which uses energy-dependent coincidence counters between a pixel-of-interest (POI) and its neighboring pixels and keeps the book of charge sharing events. A Monte Carlo (MC) simulation study was performed to assess the performance of MEICC; however, the performance might have been overestimated in a previous study. The charge sharing increases the number of photons recorded at a PCD pixel at the expense of the spatial resolution and the effect on the spatial resolution was not taken into account. The aims of this study were, first, to outline a spatially-resolved irradiation scheme for a normalized spatial resolution, and second, to assess the performance of MEICC. The MC program was modified to set the x-ray spectrum and intensity for the POI and those for the neighboring pixels separately. Data were then generated by varying two basis materials, water and bone, by a small amount only for the POI, while those for neighboring pixels remained unchanged. Cramer–Rao lower bound (CRLB) of water and bone estimation was computed from the changes in the mean and covariance matrix estimated. This setting allowed for assessing the CRLB at the same spatial resolution regardless of with or without charge sharing. The CRLBs at the normalized spatial resolution were worse than those at not-normalized spatial resolutions. With eight energy windows, MEICC provided the CRLB comparable to the ideal PCD with no charge sharing. The proposed MEICC has a potential to address charge sharing in PCDs.

Photon counting detector (PCD)-based computed tomography exploits spectral information from a transmitted x-ray spectrum to estimate basis line-integrals. The recorded spectrum, however, is distorted and deviates from the transmitted spectrum due to spectral response effect (SRE). Therefore, the SRE needs to be compensated for when estimating basis line-integrals. One approach is to incorporate the SRE model with an incident spectrum into the PCD measurement model and the other approach is to perform a calibration process that inherently includes both the SRE and the incident spectrum. A maximum likelihood estimator can be used to the former approach, which guarantees asymptotic optimality; however, a heavy computational burden is a concern. Calibration-based estimators are a form of the latter approach. They can be very efficient; however, a heuristic calibration process needs to be addressed. In this paper, we propose a computationally efficient three-step estimator for the former approach using a low-order polynomial approximation of x-ray transmittance. The low-order polynomial approximation can change the original non-linear estimation method to a two-step linearized approach followed by an iterative bias correction step. We show that the calibration process is required only for the bias correction step and prove that it converges to the unbiased solution under practical assumptions. Extensive simulation studies validate the proposed method and show that the estimation results are comparable to those of the ML estimator while the computational time is reduced substantially.

Purpose: An x-ray photon interacts with photon counting detectors (PCDs) and generates an electron charge cloud or multiple clouds. The clouds (thus, the photon energy) may be split between two adjacent PCD pixels when the interaction occurs near pixel boundaries, producing a count at both of the pixels. This is called double-counting with charge sharing. (A photoelectric effect with K-shell fluorescence x-ray emission would result in double-counting as well). As a result, PCD data are spatially and energetically correlated, although the output of individual PCD pixels is Poisson distributed. Major problems include the lack of a detector noise model for the spatio-energetic cross talk and lack of a computationally efficient simulation tool for generating correlated Poisson data. A Monte Carlo (MC) simulation can accurately simulate these phenomena and produce noisy data; however, it is not computationally efficient. Methods: In this study, the authors developed a new detector model and implemented it in an efficient software simulator that uses a Poisson random number generator to produce correlated noisy integer counts. The detector model takes the following effects into account: (1) detection efficiency; (2) incomplete charge collection and ballistic effect; (3) interaction with PCDs via photoelectric effect (with or without K-shell fluorescence x-ray emission, which may escape from the PCDs or be reabsorbed); and (4) electronic noise. The correlation was modeled by using these two simplifying assumptions: energy conservation and mutual exclusiveness. The mutual exclusiveness is that no more than two pixels measure energy from one photon. The effect of model parameters has been studied and results were compared with MC simulations. The agreement, with respect to the spectrum, was evaluated using the reduced χ2 statistics or a weighted sum of squared errors, χred2(≥1), where χred2=1 indicates a perfect fit. Results: The model produced spectra with flat field irradiation that qualitatively agree with previous studies. The spectra generated with different model and geometry parameters allowed for understanding the effect of the parameters on the spectrum and the correlation of data. The agreement between the model and MC data was very strong. The mean spectra with 90 keV and 140 kVp agreed exceptionally well: χred2 values were 1.049 with 90 keV data and 1.007 with 140 kVp data. The degrees of cross talk (in terms of the relative increase from single pixel irradiation to flat field irradiation) were 22% with 90 keV and 19% with 140 kVp for MC simulations, while they were 21% and 17%, respectively, for the model. The covariance was in strong agreement qualitatively, although it was overestimated. The noisy data generation was very efficient, taking less than a CPU minute as opposed to CPU hours for MC simulators. Conclusions: The authors have developed a novel, computationally efficient PCD model that takes into account double-counting and resulting spatio-energetic correlation between PCD pixels. The MC simulation validated the accuracy.

Smaller pixels sizes of x-ray photon counting detectors (PCDs) have the two conflicting effects as follows. On one hand, smaller pixel sizes improve the ability to handle high count rates of x-rays (i.e., pulse pileups) because incident rates onto each PCD pixel decreases with decreasing the size. On the other hand, smaller pixel sizes increase chances of crosstalk and double-counting (or n-tuple-counting in general) between neighboring pixels, because, while the same size of electron charge cloud generated by a photon is independent of PCD sizes, the charge cloud size relative to the PCD size increases with decreasing the PCD size. In addition, the following two aspects are practical configurations in actual PCD computed tomography systems: N×N-pixel binning and anti-scatter grids. When n-tuple-counting occurs and those data are binned/added during post-acquisition process, the variance of the data will be larger than its mean. The anti-scatter grids may eliminate or decrease the cross-talk and n-tuple-counting by blocking primary x-rays near pixel boundaries or for the width of one pixel entirely. In this study, we studied the effects of PCD pixel sizes, N×N-pixel binning, and pixel masking on soft tissue contrast visibility using newly developed Photon Counting Toolkit (PcTK version 3.2; https://pctk.jhu.edu).

Purpose Methods Smaller pixel sizes of x-ray photon counting detectors (PCDs) benefit count rate capabilities but increase cross-talk and "double-counting" between neighboring PCD pixels. When an x-ray photon produces multiple (n) counts at neighboring (sub-)pixels and they are added during post-acquisition N x N binning process, the variance of the final PCD output-pixel will be larger than its mean. In the meantime, anti-scatter grids are placed at the pixel boundaries in most of x-ray CT systems and will decrease cross-talk between sub-pixels because the grids mask sub-pixels underneath them, block the primary x-rays, and increase the separation distance between active sub-pixels. The aim of this paper was, first, to study the PCD statistics with various N x N binning schemes and three different masking methods in the presence of cross-talks, and second, to assess one of the most fundamental performances of x-ray CT: soft tissue contrast visibility. We used a PCD cross-talk model (Photon counting toolkit, PcTK) and produced cross-talk data between 3 x 3 neighboring sub-pixels and calculated the mean, variance, and covariance of output-pixels with each of N x N binning scheme [4 x 4 binning, 2 x 2 binning, and 1 x 1 binning (i.e., no binning)] and three different sub-pixel masking methods (no mask, 1-D mask, and 2-D mask). We then set up simulation to evaluate the soft tissue contrast visibility. X-rays of 120 kVp were attenuated by 10-40 cm-thick water, with the right side of PCDs having 0.5 cm thicker water than the left side. A pair of output-pixels across the left-right boundary were used to assess the sensitivity index (SI or d '), which typically ranges 0-1 and is a generalized signal-to-noise ratio and a statistics used in signal detection theory. Results Conclusion Binning a larger number of sub-pixels resulted in larger mean counts and larger variance-to-mean ratio when the lower threshold of the energy window was lower than the half of the incident energy. Mean counts are in the order of no mask (the largest), 1-D mask, and 2-D mask but the difference in variance-to-mean ratio was small. For a given sub-pixel size and masking method, binning more sub-pixels degraded the normalized SI values but the difference between 4 x 4 binning and 1 x 1 binning was typically less than 0.06. 1-D mask provided better normalized SI values than no mask and 2-D mask for side-by-side case and the improvements were larger with fewer binnings, although the difference was less than 0.10. 2-D mask was the best for embedded case. The normalized SI values of combined binning, sub-pixel size, and masking were in the order of 1 x 1 (900 mu m)(2) binning, 2 x 2 (450 mu m)(2) binning, and 4 x 4 (225 mu m)(2) binning for a given masking method but the difference between each of them were typically 0.02-0.05. We have evaluated the effect of double-counting between PCD sub-pixels with various binning and masking methods. SI values were better with fewer number of binning and larger sub-pixels. The difference among various binning and masking methods, however, was typically less than 0.06, which might result in a dose penalty of 13% if the CT system were linear.

Purpose The interpixel cross-talk of energy-sensitive photon counting x-ray detectors (PCDs) has been studied and an analytical model (version 2.1) has been developed for double-counting between neighboring pixels due to charge sharing and K-shell fluorescence x-ray emission followed by its reabsorption (Taguchi K, et al., Medical Physics 2016;43(12):6386-6404). While the model version 2.1 simulated the spectral degradation well, it had the following problems that has been found to be significant recently: (1) The spectrum is inaccurate with smaller pixel sizes; (2) the charge cloud size must be smaller than the pixel size; (3) the model underestimates the spectrum/counts for 10-40 keV; and (4) the model version 2.1 cannot handlen-tuple-counting withn > 2 (i.e., triple-counting or higher). These problems are inherent to the design of the model version 2.1; therefore, we developed a new model and addressed these problems in this study. Methods We propose a new PCD cross-talk model (version 3.2; Pc TK for "photon counting toolkit") that is based on a completely different design concept from the previous version. It uses a numerical approach and starts with a 2-D model of charge sharing (as opposed to an analytical approach and a 1-D model with version 2.1) and addresses all of the four problems. The model takes the following factors into account: (1) shift-variant electron density of the charge cloud (Gaussian-distributed), (2) detection efficiency, (3) interactions between photons and PCDs via photoelectric effect, and (4) electronic noise. Correlated noisy PCD data can be generated using either a multivariate normal random number generator or a Poisson random number generator. The effect of the two parameters, the effective charge cloud diameter (d0 ) and pixel size (dpix ), was studied and results were compared with Monte Carlo simulations and the previous model version 2.1. Finally, a script for the workflow for CT image quality assessment has been developed, which started with a few material density images, generated material-specific sinogram (line integrals) data, noisy PCD data with spectral distortion using the model version 3.2, and reconstructed PCD- CT images for four energy windows. Results The model version 3.2 addressed all of the four problems listed above. The spectra withdpix = 56-113 μm agreed with that of Medipix3 detector withdpix = 55-110 μm without charge summing mode qualitatively. The counts for 10-40 keV were larger than the previous model (version 2.1) and agreed with MC simulations very well (root-mean-square difference values with model version 3.2 were decreased to 16%-67% of the values with version 2.1). There were many non-zero off-diagonal elements withn-tuple-counting withn > 2 in the normalized covariance matrix of 3 × 3 neighboring pixels. Reconstructed images showed biases and artifacts attributed to the spectral distortion due to the charge sharing and fluorescence x rays. Conclusion We have developed a new PCD model for spatio-energetic cross-talk and correlation between PCD pixels. The workflow demonstrated the utility of the model for general or task-specific image quality assessments for the PCD- CT.Note: The program (Pc TK) and the workflow scripts have been made available to academic researchers. Interested readers should visit the website (pctk.jhu.edu) or contact the corresponding author.

This study concerns how to model x-ray transmittance, exp (- integral mu(a)(r, E)dr), of the object using a small number of energy-dependent bases, which plays an important role for estimating basis line-integrals in photon counting detector (PCD)-based computed tomography (CT). Recently, we found that low-order polynomials can model the smooth x-ray transmittance, i.e. object without contrast agents, with sufficient accuracy, and developed a computationally efficient three-step estimator. The algorithm estimates the polynomial coefficients in the first step, estimates the basis line-integrals in the second step, and corrects for bias in the third step. We showed that the three-step estimator was similar to 1, 500 times faster than conventional maximum likelihood (ML) estimator while it provided comparable bias and noise. The three-step estimator was derived based on the modeling of x-ray transmittance;thus, the accurate modeling of x-ray transmittance is an important issue. For this purpose, we introduce a modeling of the x-ray transmittance via dictionary learning approach. We show that the relative modeling error of dictionary learning-based approach is smaller than that of the low-order polynomials.

Energy-sensitive photon counting detectors (PCDs) have recently been developed for medical X-ray computed tomography (CT) imaging and a handful of prototype PCD-CT systems have been built and evaluated. PCDs detect X-rays by using mechanisms that are completely different from the current CT detectors (i.e., energy integrating detectors or EIDs); PCDs count photons and obtain the information of the object tissues (i.e., the effective atomic numbers and mass densities) to be imaged. Therefore, these PCDs have the potential not only for evolution-to improve the current CT images such as providing dose reduction-but also for a revolution-to enable novel applications with a new concept such as molecular CT imaging. The performance of PCDs, however, is not flawless, and thus, it requires integrated efforts to develop PCD-CT for clinical use. In this article, we review the current status and the prediction for the future of PCDs, PCD-CT systems, and potential clinical applications.

For myocardial perfusion CT exams, beam hardening (BH) artifacts may degrade the accuracy of myocardial perfusion defect detection. Meanwhile, cardiac motion may make BH process inconsistent, which makes conventional BH correction (BHC) methods ineffective. The aims of this study were to assess the severity of BH artifacts and motion artifacts and propose a projection-based iterative BHC method which has a potential to handle the motion-induced inconsistency better than conventional methods. In this study, four sets of forward projection data were first acquired using both cylindrical phantoms and cardiac images as objects: (1) with monochromatic x-rays without motion; (2) with polychromatic x-rays without motion; (3) with monochromatic x-rays with motion; and (4) with polychromatic x-rays with motion. From each dataset, images were reconstructed using filtered back projection; for datasets 2 and 4, one of the following BHC methods was also performed: (A) no BHC; (B) BHC that concerns water only; and (C) BHC that takes both water and iodine into account, which is an iterative method we developed in this work. Biases of images were quantified by the mean absolute difference (MAD). The MAD of images with BH artifacts alone (dataset 2, without BHC) was comparable or larger than that of images with motion artifacts alone (dataset 3): In the study of cardiac image, BH artifacts account for over 80% of the total artifacts. The use of BHC was effective: with dataset 4, MAD values were 170 HU with no BHC, 54 HU with water BHC, and 42 HU with the proposed BHC. Qualitative improvements in image quality were also noticeable in reconstructed images.

An x-ray photon interacts with photon counting detectors (PCDs) and generates an electron charge cloud or multiple clouds. The clouds (thus, the photon energy) may be split between two adjacent PCD pixels when the interaction occurs near pixel boundaries, producing a count at both of the two pixels. This is called double-counting with charge sharing. The output of individual PCD pixel is Poisson distributed integer counts; however, the outputs of adjacent pixels are correlated due to double-counting. Major problems are the lack of detector noise model for the spatio-energetic crosstalk and the lack of an efficient simulation tool. Monte Carlo simulation can accurately simulate these phenomena and produce noisy data; however, it is not computationally efficient. In this study, we developed a new detector model and implemented into an efficient software simulator which uses a Poisson random number generator to produce correlated noisy integer counts. The detector model takes the following effects into account effects: (1) detection efficiency and incomplete charge collection; (2) photoelectric effect with total absorption; (3) photoelectric effect with fluorescence x-ray emission and re-absorption; (4) photoelectric effect with fluorescence x-ray emission which leaves PCD completely; and (5) electric noise. The model produced total detector spectrum similar to previous MC simulation data. The model can be used to predict spectrum and correlation with various different settings. The simulated noisy data demonstrated the expected performance: (a) data were integers; (b) the mean and covariance matrix was close to the target values; (c) noisy data generation was very efficient

Purpose: The objective of the study was to demonstrate that, in x-ray computed tomography (CT), more than two types of materials can be effectively separated with the use of an energy resolved photon-counting detector and classification methodology. Specifically, this applies to the case when contrast agents that contain K-absorption edges in the energy range of interest are present in the object. This separation is enabled via the use of recently developed energy resolved photon-counting detectors with multiple thresholds, which allow simultaneous measurements of the x-ray attenuation at multiple energies. Methods: To demonstrate this capability, we performed simulations and physical experiments using a six-threshold energy resolved photon-counting detector. We imaged mouse-sized cylindrical phantoms filled with several soft-tissue-like and bone-like materials and with iodine-based and gadolinium-based contrast agents. The linear attenuation coefficients were reconstructed for each material in each energy window and were visualized as scatter plots between pairs of energy windows. For comparison, a dual-kVp CT was also simulated using the same phantom materials. In this case, the linear attenuation coefficients at the lower kVp were plotted against those at the higher kVp. Results: In both the simulations and the physical experiments, the contrast agents were easily separable from other soft-tissue-like and bone-like materials, thanks to the availability of the attenuation coefficient measurements at more than two energies provided by the energy resolved photon-counting detector. In the simulations, the amount of separation was observed to be proportional to the concentration of the contrast agents; however, this was not observed in the physical experiments due to limitations of the real detector system. We used the angle between pairs of attenuation coefficient vectors in either the 5-D space (for non-contrast-agent materials using energy resolved photon-counting acquisition) or a 2-D space (for contrast agents using energy resolved photon-counting acquisition and all materials using dual-kVp acquisition) as a measure of the degree of separation. Compared to dual-kVp techniques, an energy resolved detector provided a larger separation and the ability to separate different target materials using measurements acquired in different energy window pairs with a single x-ray exposure. Conclusions: We concluded that x-ray CT with an energy resolved photon-counting detector with more than two energy windows allows the separation of more than two types of materials, e.g., soft-tissue-like, bone-like, and one or more materials with K-edges in the energy range of interest. Separating material types using energy resolved photon-counting detectors has a number of advantages over dual-kVp CT in terms of the degree of separation and the number of materials that can be separated simultaneously.

Purpose: Recently, photon counting x-ray detectors (PCXDs) with energy discrimination capabilities have been developed for potential use in clinical computed tomography (CT) scanners. These PCXDs have great potential to improve the quality of CT images due to the absence of electronic noise and weights applied to the counts and the additional spectral information. With high count rates encountered in clinical CT, however, coincident photons are recorded as one event with a higher or lower energy due to the finite speed of the PCXD. This phenomenon is called a ''pulse pileup event'' and results in both a loss of counts (called ''deadtime losses'') and distortion of the recorded energy spectrum. Even though the performance of PCXDs is being improved, it is essential to develop algorithmic methods based on accurate models of the properties of detectors to compensate for these effects. To date, only one PCXD (model DXMCT-1, DxRay, Inc., Northridge, CA) has been used for clinical CT studies. The aim of that study was to evaluate the agreement between data measured by DXMCT-1 and those predicted by analytical models for the energy response, the deadtime losses, and the distorted recorded spectrum caused by pulse pileup effects. Methods: An energy calibration wasmore » performed using {sup 99m}Tc (140 keV), {sup 57}Co (122 keV), and an x-ray beam obtained with four x-ray tube voltages (35, 50, 65, and 80 kVp). The DXMCT-1 was placed 150 mm from the x-ray focal spot; the count rates and the spectra were recorded at various tube current values from 10 to 500 {mu}A for a tube voltage of 80 kVp. Using these measurements, for each pulse height comparator we estimated three parameters describing the photon energy-pulse height curve, the detector deadtime {tau}, a coefficient k that relates the x-ray tube current I to an incident count rate a by a=kxI, and the incident spectrum. The mean pulse shape of all comparators was acquired in a separate study and was used in the model to estimate the distorted recorded spectrum. The agreement between data measured by the DXMCT-1 and those predicted by the models was quantified by the coefficient of variation (COV), i.e., the root mean square difference divided by the mean of the measurement. Results: Photon energy versus pulse height curves calculated with an analytical model and those measured using the DXMCT-1 were in agreement within 0.2% in terms of the COV. The COV between the output count rates measured and those predicted by analytical models was 2.5% for deadtime losses of up to 60%. The COVs between spectra measured and those predicted by the detector model were within 3.7%-7.2% with deadtime losses of 19%-46%. Conclusions: It has been demonstrated that the performance of the DXMCT-1 agreed exceptionally well with the analytical models regarding the energy response, the count rate, and the recorded spectrum with pulse pileup effects. These models will be useful in developing methods to compensate for these effects in PCXD-based clinical CT systems.« less

Purpose: Recently, novel CdTe photon counting x-ray detectors (PCXDs) with energy discrimination capabilities have been developed. When such detectors are operated under a high x-ray flux, however, coincident pulses distort the recorded energy spectrum. These distortions are called pulse pileup effects. It is essential to compensate for these effects on the recorded energy spectrum in order to take full advantage of spectral information PCXDs provide. Such compensation can be achieved by incorporating a pileup model into the image reconstruction process for computed tomography, that is, as a part of the forward imaging process, and iteratively estimating either the imaged object or the line integrals using, e.g., a maximum likelihood approach. The aim of this study was to develop a new analytical pulse pileup model for both peak and tail pileup effects for nonparalyzable detectors. Methods: The model takes into account the following factors: The bipolar shape of the pulse, the distribution function of time intervals between random events, and the input probability density function of photon energies. The authors used Monte Carlo simulations to evaluate the model. Results: The recorded spectra estimated by the model were in an excellent agreement with those obtained by Monte Carlo simulations for various levels of pulse pileup effects. The coefficients of variation (i.e., the root mean square difference divided by the mean of measurements) were 5.3%–10.0% for deadtime losses of 1%–50% with a polychromatic incident x-ray spectrum. Conclusions: The proposed pulse pileup model can predict recorded spectrum with relatively good accuracy.

We describe the effect of the off-center position, the bowtie filter type, and the direction of scan projection radiograph on the radiation dose and image noise of 64-detector computed tomographic scans using the automatic tube current modulation technique. On anteroposterior scan projection radiographs, the tube current ratio increased, with an increase in the off-center position of the phantom irrespective of the filter size. On lateral scan projection radiographs, it remained constant with each bowtie filter type regardless of the off-center phantom position.

Purpose: Photon counting x-ray detectors (PCXDs) are an important emerging technology for spectral imaging and material differentiation with numerous potential applications in diagnostic imaging. We report development of a Si-strip PCXD system originally developed for mammography with potential application to spectral CT of musculoskeletal extremities, including challenges associated with sparse sampling, spectral calibration, and optimization for higher energy x-ray beams. Methods: A bench-top CT system was developed incorporating a Si-strip PCXD, fixed anode x-ray source, and rotational and translational motions to execute complex acquisition trajectories. Trajectories involving rotation and translation combined with iterative reconstruction were investigated, including single and multiple axial scans and longitudinal helical scans. The system was calibrated to provide accurate spectral separation in dual-energy three-material decomposition of soft-tissue, bone, and iodine. Image quality and decomposition accuracy were assessed in experiments using a phantom with pairs of bone and iodine inserts (3, 5, 15 and 20 mm) and an anthropomorphic wrist. Results: The designed trajectories improved the sampling distribution from 56% minimum sampling of voxels to 75%. Use of iterative reconstruction (viz., penalized likelihood with edge preserving regularization) in combination with such trajectories resulted in a very low level of artifacts in images of the wrist. For large bone or iodine inserts (>5 mm diameter), the error in the estimated material concentration was

If a multislice or other area detector is shifted to one side to cover a larger field of view, then the data are truncated on one side. We propose a method to restore the missing data in helical cone-beam acquisitions that uses measured data on the longer side of the asymmetric detector array. The method is based on the idea of complementary rays, which is well known in fan beam geometry; in this paper we extend this concept to the cone-beam case. Different cases of complementary data coverage and dependence on the helical pitch are considered. The proposed method is used in our prototype 16-row CT scanner with an asymmetric detector and a 700 mm field of view. For evaluation we used scanned body phantom data and computer-simulated data. To simulate asymmetric truncation, the full, symmetric datasets were truncated by dropping either 22.5% or 45% from one side of the detector. Reconstructed images from the prototype scanner with the asymmetrical detector show excellent image quality in the extended field of view. The proposed method allows flexible helical pitch selection and can be used with overscan, short-scan, and super-short-scan reconstructions.

Purpose: Energy discriminating, photon-counting detectors (PCDs) are an emerging technology for computed tomography (CT) with various potential benefits for clinical CT. The photon energies measured by PCDs can be distorted due to the interactions of a photon with the detector and the interaction of multiple coincident photons. These effects result in distorted recorded x-ray spectra which may lead to artifacts in reconstructed CT images and inaccuracies in tissue identification. Model-based compensation techniques have the potential to account for the distortion effects. This approach requires only a small number of parameters and is applicable to a wide range of spectra and count rates, but it needs an accurate model of the spectral distortions occurring in PCDs. The purpose of this study was to develop a model of those spectral distortions and to evaluate the model using a PCD (model DXMCT-1; DxRay, Inc., Northridge, CA) and various x-ray spectra in a wide range of count rates. Methods: The authors hypothesize that the complex phenomena of spectral distortions can be modeled by: (1) separating them into count-rate independent factors that we call the spectral response effects (SRE), and count-rate dependent factors that we call the pulse pileup effects (PPE), (2) developing separate models for SRE and PPE, and (3) cascading the SRE and PPE models into a combined SRE+PPE model that describes PCD distortions at both low and high count rates. The SRE model describes the probability distribution of the recorded spectrum, with a photo peak and a continuum tail, given the incident photon energy. Model parameters were obtained from calibration measurements with three radioisotopes and then interpolated linearly for other energies. The PPE model used was developed in the authors’ previous work [K. Taguchi , “Modeling the performance of a photon counting x-ray detector for CT: Energy response and pulse pileup effects,” Med. Phys. 38(2), 1089–1102 (2011)]. The agreement between the x-ray spectra calculated by the cascaded SRE+PPE model and the measured spectra was evaluated for various levels of deadtime loss ratios (DLR) and incident spectral shapes, realized using different attenuators, in terms of the weighted coefficient of variation (COVW), i.e., the root mean square difference weighted by the statistical errors of the data and divided by the mean. Results: At low count rates, when DLR < 10%, the distorted spectra measured by the DXMCT-1 were in agreement with those calculated by SRE only, with COVW's less than 4%. At higher count rates, the measured spectra were also in agreement with the ones calculated by the cascaded SRE+PPE model; with PMMA as attenuator, COVW was 5.6% at a DLR of 22% and as small as 6.7% for a DLR as high as 55%. Conclusions: The x-ray spectra calculated by the proposed model agreed with the measured spectra over a wide range of count rates and spectral shapes. The SRE model predicted the distorted, recorded spectra with low count rates over various types and thicknesses of attenuators. The study also validated the hypothesis that the complex spectral distortions in a PCD can be adequately modeled by cascading the count-rate independent SRE and the count-rate dependent PPE.

Photon counting detector (PCD) x-ray imaging systems have seen increasing use in the past decade in applications such as low-dose radiography and tomography. A cascaded systems analysis model has been developed to describe the signal and noise transfer characteristics for such systems in a manner that accounts for unique PCD functionality (such as an application of a threshold) and explicitly considers the distribution of quanta through each stage. This model was used to predict the mean signal, modulation transfer function (MTF), noise-power spectrum (NPS), and detective quantum efficiency (DQE) of a silicon-strip PCD system, and these predictions were compared to measurements across a range of exposure conditions and thresholds. Further, the model was used to investigate the impact of design parameters such as detector thickness and pulse height amplification as well as unique PCD performance effects such as charge sharing and additive noise with respect to threshold. The development of an analytical model for prediction of such metrics provides a framework for understanding the complex imaging performance characteristics of PCD systems – especially important in the early development of new radiographic and tomographic applications – and a guide to task-based performance optimization.

Photon counting detectors are an emerging technology for spectral computed tomography. They have the potential to improve tissue contrast and specificity, reduce dose, and enable novel applications for K-edge and functional imaging. In this presentation various non-linear distortions were investigated that affect the image quality in photon-counting spectral CT: deadtime losses and spectral response, inherent to the new technology, and beam hardening artifacts that stem from the use of a polychromatic x-ray source. These effects were corrected or compensated for by performing calibration measurements. Techniques from material decomposition were applied to reconstruct images at a desired energy. Two methods were compared to synthesize a single monoenergetic image from photon counting data with multiple energy bins. The parameters were optimized to maximize a given image quality index. The procedures were evaluated on phantom data acquired on an experimental CT scanner with photon-counting detectors with two energy thresholds.

Photon counting statistics with pulse pileup effects (PPE) have been investigated for detection schemes with two assumptions: a fixed deadtime (i.e., non-paralyable and paralyzable detection schemes) and a delta pulse shape. Analytical expressions have been developed which shed light on interesting findings: (1) the variance becomes smaller than mean with PPE; and (2) the variance-to-mean ratio (VMR) of narrow energy windows remains very close to 1. In this study, we experimentally investigate VMR with PPE with a variable deadtime (i.e., pulse height analysis) and bipolar and unipolar pulse shapes with a long tail in addition to the above cases. We will use Monte Carlo simulation for a systematic study and a physical photon counting detector to confirm the results.

Photon counting x-ray detectors (PCXDs) are an emerging technology in x-ray computed tomography (CT) as they have the potential to overcome some of the most significant limitations of current CT with energy integrating detectors. Among these are: insufficient tissue contrast, relatively high radiation dose, tissue non-specificity, and the non-quantitative nature. In contrast, CT with PCXDs has shown promise in producing higher contrast, tissue specific, quantitative images at lower dose. Novel applications for PCXDs include k-edge and functional imaging and material decomposition. A limiting factor, however, is the high photon flux that occurs in clinical applications resulting in signal pulse pile up in the detector. Faster detectors and new strategies for data corrections and image reconstruction algorithms are needed to overcome these limitations. A research tabletop x-ray CT scanner was developed with the following aims: 1) to characterize and calibrate the PCXD; 2) to acquire CT projection data under conditions similar to those of clinical CT; and 3) to reconstruct images using correction schemes specific for PCXDs. The scanner employs a commercial clinical x-ray tube, a PCXD with two energy thresholds, and allows scanning of objects of up to 40 cm in diameter. This paper presents measurements of detector quantities crucial for data corrections and calibration, such as energy response, deadtime, and count rates. Reconstructed CT images are presented and qualitative results from material decomposition are shown.

Energy sensitive photon counting x-ray detectors (PCXD) [1] have many advantages over energy-integrating x-ray detectors (EIXD) in x-ray computed tomography (CT), such as the ability to measure the spectrum of x-ray beams. When such PCXDs are operated under a high count rate in clinical scanners, coincident photons would distort the recorded energy spectrum due to the limited speed of the detector. To compensate for the spectrum distortions, we have developed analytical models for them [3] and integrated one such model into an image reconstruction process using a sinogram restoration framework [6]. In this method, the attenuation of the object was modeled as a sum of line integrals of N basis functions, where N was fixed at 3 for the entire sinogram when a contrast agent is involved. The method allowed us to reconstruct accurate images, compensating for the effect of spectrum distortion of PCXD; however, the contrast-to-noise (CNR) of the images were only comparable to that obtained by EIXDs. We believe the main reason is an increased statistical uncertainty in the estimated line integrals introduced by the 3rd basis function. In this paper, we propose a method to improve the CNR by employing the fewest number of basis functions N m (≤ N) as necessary for an individual sinogram ray. Our simulation studies indicate that the CNR achieved for a Gd-based contrast agent by PCXDs could be 12% better than the conventional method of [6], and 28% better than EIXDs for scans with similar number of x-ray photons, which points to a dose reduction of 20% and 39% respectively.

Recently, novel CdTe photon counting x-ray detectors (PCXDs) with energy discrimination capabilities have been developed. When such detectors are operated under a high x-ray flux, however, coincident pulses distort the recorded energy spectrum. These distortions are called pulse pileup effects. It is essential to compensate for these effects on the recorded energy spectrum in order to take full advantage of spectral information PCXDs provide. Such compensation can be achieved by incorporating a pileup model into the image reconstruction process for computed tomography, that is, as a part of the forward imaging process, and iteratively estimating either the imaged object or the line integrals using, e.g., a maximum likelihood approach. The aim of this study was to develop a new analytical pulse pileup model for both peak and tail pileup effects for nonparalyzable detectors.The model takes into account the following factors: The bipolar shape of the pulse, the distribution function of time intervals between random events, and the input probability density function of photon energies. The authors used Monte Carlo simulations to evaluate the model.The recorded spectra estimated by the model were in an excellent agreement with those obtained by Monte Carlo simulations for various levels of pulse pileup effects. The coefficients of variation (i.e., the root mean square difference divided by the mean of measurements) were 5.3%-10.0% for deadtime losses of 1%-50% with a polychromatic incident x-ray spectrum.The proposed pulse pileup model can predict recorded spectrum with relatively good accuracy.

Photon counting x-ray detectors (PCXDs) with energy discrimination capabilities offer various advantages over the current intensity integrating detectors, such as improved accuracy in material decomposition, reduced image noise, reduced radiation dose, etc. The major problem of PCXDs, however, is the limited speed. The required count rate for clinical x-ray CT scanners may be 109 counts-per-second-per-square-millimeters (cps), while the operational count rates (where a count rate loss is less than 5%) of available PCXDs are much lower, e.g., 5 × 105 cps. In this study, we propose to enable PCXD-based clinical CT imaging using these slower-than-desired detectors by a combination of four methods that reduce the count rate requirements and compensate for the effect of pileup.

We report on a characterization study of a multi-row direct-conversion x-ray detector used to generate the first photon counting clinical x-ray computed tomography (CT) patent images. In order to provide the photon counting detector with adequate performance for low-dose CT applications, we have designed and fabricated a fast application specific integrated circuit (ASIC) for data readout from the pixellated CdTe detectors that comprise the photon counting detector. The cadmium telluride (CdTe) detector has 512 pixels with a 1 mm pitch and is vertically integrated with the ASIC readout so it can be tiled in two dimensions similar to those that are tiled in an arc found in 32-row multi-slice CT systems. We have measured several important detector parameters including the maximum output count rate, energy resolution, and noise performance. Additionally the relationship between the output and input rate has been found to fit a non-paralyzable detector model with a dead time of 160 nsec. A maximum output rate of 6 × 106 counts per second per pixel has been obtained with a low output x-ray tube for CT operated between 0.01 mA and 6 mA at 140 keV and different source-to-detector distances. All detector noise counts are less that 20 keV which is sufficiently low for clinical CT. The energy resolution measured with the 60 keV photons from a 241Am source is ~12%. In conclusion, our results demonstrate the potential for the application of the CdTe based photon counting detector to clinical CT systems. Our future plans include further performance improvement by incorporating drift structures to each detector pixel.

This work aims at discriminating between soft and calcified coronary artery plaques using microCT with a multi-energywindow photon counting X-ray detector (PCXD). We have previously investigated a solid state X-ray detector which has the capability to count individual photons in different energy windows. The data from these energy windows may be treated as multiple simultaneous X-ray acquisitions within non-overlapping energy windows that can provide additional information about tissue differences. In this work, we simulated a photon counting detector with five energy windows. We investigated two approaches for using the energy information provided by this detector. First, we applied energy weighting to the reconstruction from different energy windows to improve the signal-to-noise ratio between calcified and soft plaques. This resulted in a significant improvement in the signal-to-noise ratio. Second, we applied the basis material decomposition method to discriminate coronary artery plaques based on their calcium content. The results were compared with those obtained using dual-kVp material decomposition. We observed significantly improved contrast-tonoise ratios for the PCXD-based approaches.

We have developed and evaluated a method to correct for detector cell response variations in photon-counting X-ray detectors with energy discrimination capability. With these detectors, variations in energy thresholds or energy response of the detector cells can result in spectral-dependent non-uniformities in sinograms that produce rings in reconstructed images. The proposed method is basis material decomposition-based and corrects variations in the spectral sensitivity of detector cells to reflect the characteristics of a standard detector cell. It requires calibration similar to that used in basis material decomposition methods and does not require knowledge of the exact energy spectrum, energy thresholds, or energy response of the individual detector cells. Both simulation and physical experiments studies showed substantial reduction in non-uniformity in sinograms and of rings in reconstructed images.

One of problems with the current cardiac CT imaging is the banding artifacts, i.e., horizontal shifts in multiplanar reformatted (MPR) or three-dimensional (3-D) images. In this work, we propose a novel gating method that does not rely on electro-cardiogram but uses the similarity of image pixel values of heart images. Moreover, the proposed method optimizes the cardiac phase on a local basis. Evaluations with 10 patient data sets showed the substantial reduction of banding artifacts as well as the improved consistency in anatomical structures.

In this study, we propose to estimate time-dependent attenuation curves on region-of-interest basis using a priori and projection data acquired without gantry rotation.

application/pdf, We develop an approximate fan-beam algorithm to reconstruct an object with time-dependent nonrigid transformation such as the heart. The method is in the form of derivative backprojection filtering with compensation of affine transformations on a local basis. Computer simulations showed the proposed method significantly reduces image artifact due to nonrigid motion. Therefore, with very little motion artifact, the proposed method allowed us to reconstruct images from projections over about one motion cycle, resulting in reduced image noise level down to 40% of the current level.

In this work we used a novel CdTe photon counting x-ray detector capable of very high count rates to perform x-ray micro-computed tomography (microCT). The detector had 2 rows of 384 square pixels each 1 mm in size. Charge signals from individual photons were integrated with a shaping time of ~60 ns and processed by an ASIC located in close proximity to the pixels. The ASIC had 5 energy thresholds with associated independent counters for each pixel. Due to the thresholding, it is possible to eliminate dark-current contributions to image noise. By subtracting counter outputs from adjacent thresholds, it is possible to obtain the number of x-ray photon counts in 5 adjacent energy windows. The detector is capable of readout times faster than 5 ms. A prototype bench-top specimen μCT scanner was assembled having distances from the tube to the object and detector of 11 cm and 82 cm, respectively. We used a conventional x-ray source to produce 80 kVp x-ray beams with tube currents up to 400 μA resulting in count rates on the order of 600 kcps per pixel at the detector. Both phantoms and a dead mouse were imaged using acquisition times of 1.8 s per view at 1° steps around the object. The count rate loss (CRL) characteristics of the detector were measured by varying the tube current and corrected for using a paralyzable model. Images were reconstructed using analytical fan-beam reconstruction. The reconstructed images showed good contrast and noise characteristics and those obtained from different energy windows demonstrated energy-dependent contrast, thus potentially allowing for material decomposition.

Novel CdTe photon counting x-ray detectors (PCXDs) have been developed for very high count rates [1-4] suitable for x-ray micro computed tomography (μCT) scanners. It counts photons within each of J energy bins. In this study, we investigate use of the data in these energy bins for material decomposition using an image domain approach. In this method, one image is reconstructed from projection data of each energy bin; thus, we have J images from J energy bins that are associated with attenuation coefficients with a narrow energy width. We assume that the spread of energies in each bin is small and thus that the attenuation can be modeled using an effective energy for each bin. This approximation allows us to linearize the problem, thus simplify the inversion procedure. We then fit J attenuation coefficients at each location x by the energy-attenuation function [5] and obtain either (1) photoelectric and Compton scattering components or (2) 2 or 3 basis-material components. We used computer simulations to evaluate this approach generating projection data with three types of acquisition schemes: (A) five monochromatic energies; (B) five energy bins with PCXD and an 80 kVp polychromatic x-ray spectrum; and (C) two kVp with an intensity integrating detector. Total attenuation coefficients of reconstructed images and calculated effective atomic numbers were compared with data published by National Institute of Standards and Technology (NIST). We developed a new materially defined "SmileyZ" phantom to evaluate the accuracy of the material decomposition methods. Preliminary results showed that material based 3-basis functions (bone, water and iodine) with PCXD with 5 energy bins was the most promising approach for material decomposition.

Recently developed solid-state detectors combined with high-speed ASICs that allow individual pixel pulse processing may prove useful as detectors for small animal micro-computed tomography. One appealing feature of these photon-counting x-ray detectors (PCXDs) is their ability to discriminate between photons with different energies and count them in a small number (2-5) of energy windows. The data in these energy windows may be thought of as arising from multiple simultaneous x-ray beams with individual energy spectra, and could thus potentially be used to perform material composition analysis. The goal of this paper was to investigate the potential advantages of PCXDs with multiple energy window counting capability as compared to traditional integrating detectors combined with acquisition of images using x-ray beams with 2 different kVps. For the PCXDs, we investigated 3 potential sources of crosstalk: scatter in the object and detector, limited energy resolution, and pulse piluep. Using Monte Carlo simulations, we showed that scatter in the object and detector results in relatively little crosstalk between the data in the energy windows. To study the effects of energy resolution and pulse-pileup, we performed simulations evaluating the accuracy and precision of basis decomposition using a detector with 2 or 5 energy windows and a single kVp compared to an dual kVp acquisitions with an integrating detector. We found that, for noisy data, the precision of estimating the thickness of two basis materials for a range of material compositions was better for the single kVp multiple energy window acquisitions compared to the dual kVp acquisitions with an integrating detector. The advantage of the multi-window acquisition was somewhat reduced when the energy resolution was reduced to 10 keV and when pulse pileup was included, but standard deviations of the estimated thicknesses remained better by more than a factor of 2.

Two major problems with the current electrocardiogram-gated cardiac CT imaging technique are a large patient radiation dose and insufficient temporal resolution. Our long-term goal is to develop new time resolved and low dose cardiac CT imaging techniques that consist of image reconstruction algorithms and estimation methods of the time-dependent motion vector field of the heart from the acquired CT data. Toward this goal, we developed a method that estimates the 2D components of the motion vector field from a sequence of cardiac CT images.

A method of increasing the efficiency of hardware-based circular and helical cone beam x-Ray CT reconstruction is presented. During reconstruction, an image slice at any arbitrary axial position is created by backprojecting reconstructed image pixels to corresponding positions on the detector array. This is computationally inefficient for cylindrical arrays because the backprojection equations for the channel and segment positions involve time-consuming arctangent calculations. Since the detector array matrix is smaller than the reconstruction matrix, backprojection speed can be increased if the system geometry is changed so that the arctangent calculations are performed on the detector array matrix rather than the reconstruction matrix. The most efficient configuration is where a row of reconstructed image pixels projects to a single row of detector channels with constant segment number and constant spacing along the channels. This configuration can be achieved by double centering; which consists of reprojecting the original cylindrical array projection data onto a flat virtual detector located in the xz plane. A double-centering algorithm with corresponding cone-beam reconstruction algorithm has been developed and implemented on a PC for the circular case. Cone-beam circular projection data from a ball phantom has been generated by simulation, double-centered, and reconstructed. The image quality of the double-centered reconstructions has been assessed, and the details and tradeoffs of practical implementation from an image quality standpoint are discussed.

The causes of the image artifacts in a 4-slice helical computed tomography have been discussed as follows: (1) changeover in pairs of data used in z interpolation, (2) sampling interval in z, and (3) the cone angle. This study analyzes the first two causes of the artifact and describes how the current algorithm [K. Taguchi and H. Aradate, Radiology 205P, 390 (1997); 205P, 618 (1997); Med. Phys. 25, 550-561 (1998); H. Hu, ibid. 26, 5-18 (1999); S. Schaller et al., IEEE Trans. Med. Imaging 19, 822-834 (2000); K. Taguchi, Ph.D. thesis, University of Tsukuba, 2002] solves the problem. An interpolated sinogram for a slice at the edge of a ball phantom shows discontinuity caused by the changeover. If we extend the streak artifact in the reconstructed image, it crosses the focus orbit at the corresponding projection angle. Applying z filtering can reduce such causes by its feathering effect and mixing data obtained by different cone angles; the best results are provided when z filtering is applied to densely sampled helical data.

Multi-slice helical CT-systems suffer from windmill artifacts: black/white patterns that spin off of features with high longitudinal gradients. The number of black/white pairs matches the number of slices (detector rows) in the multi-slive detector. The period of spin is the same as the helical pitch. We investigate the cause of the pattern by following the traces of selected voxels through the multi-slive detector array as a function of view position. This forms an "extracted sinogram" which represents the data used to reconstruct the specific voxel. Now we can determine the cause of the artifact by correlating the windmill streak in the image with the extracted data. The investigation shows that inadequate sampling along the longitudinal direction causes the artifact.

Purpose: Photon counting detectors (PCDs) are an emerging technology with applications in spectral and low-dose radiographic and tomographic imaging. This paper develops an analytical model of PCD imaging performance, including the system gain, modulation transfer function (MTF), noise-power spectrum (NPS), and detective quantum efficiency (DQE). Methods: A cascaded systems analysis model describing the propagation of quanta through the imaging chain was developed. The model was validated in comparison to the physical performance of a silicon-strip PCD implemented on an experimental imaging bench. The signal response, MTF, and NPS were measured and compared to theory as a function of exposure conditions (70 kVp, 1–7 mA), detector threshold, and readout mode (i.e., the option for coincidence detection). The model sheds new light on the dependence of spatial resolution, charge sharing, and additive noise effects on threshold selection and was used to investigate the factors governing PCD performance, including the fundamental advantages and limitations of PCDs in comparison to energy-integrating detectors (EIDs) in the linear regime for which pulse pileup can be ignored. Results: The detector exhibited highly linear mean signal response across the system operating range and agreed well with theoretical prediction, as did the system MTF and NPS. The DQE analyzed as a function of kilovolt (peak), exposure, detector threshold, and readout mode revealed important considerations for system optimization. The model also demonstrated the important implications of false counts from both additive electronic noise and charge sharing and highlighted the system design and operational parameters that most affect detector performance in the presence of such factors: for example, increasing the detector threshold from 0 to 100 (arbitrary units of pulse height threshold roughly equivalent to 0.5 and 6 keV energy threshold, respectively), increased the f 50 (spatial-frequency at which the MTF falls to a value of 0.50) by ∼30% with corresponding improvement in DQE. The range in exposure and additive noise for which PCDs yield intrinsically higher DQE was quantified, showing performance advantages under conditions of very low-dose, high additive noise, and high fidelity rejection of coincident photons. Conclusions: The model for PCD signal and noise performance agreed with measurements of detector signal, MTF, and NPS and provided a useful basis for understanding complex dependencies in PCD imaging performance and the potential advantages (and disadvantages) in comparison to EIDs as well as an important guide to task-based optimization in developing new PCD imaging systems.

Photon counting detectors (PCDs) with energy discrimination capabilities have been developed for medical x-ray computed tomography (CT) and x-ray (XR) imaging. Using detection mechanisms that are completely different from the current energy integrating detectors and measuring the material information of the object to be imaged, these PCDs have the potential not only to improve the current CT and XR images, such as dose reduction, but also to open revolutionary novel applications such as molecular CT and XR imaging. The performance of PCDs is not flawless, however, and it seems extremely challenging to develop PCDs with close to ideal characteristics. In this paper, the authors offer our vision for the future of PCD-CT and PCD-XR with the review of the current status and the prediction of (1) detector technologies, (2) imaging technologies, (3) system technologies, and (4) potential clinical benefits with PCDs.

Purpose: To develop an analytical cascaded systems analysis (CSA) model for investigating the limits of signal and noise performance [noise‐power spectrum (NPS), modulation transfer function (MTF), and detective quantum efficiency (DQE)] of photon‐counting detectors (PCDs). Methods: Previously developed models for signal and noise propagation in flat‐panel detectors were extended to include physical effects in the imaging chain specific to the performance of PCDs, including the effect of Compton scatter in the detector, time and energy dependent effects of pulse pileup, and signal threshold. A CT imaging bench incorporating a Si‐strip PCD was constructed to test and validate the theoretical model and provide a plaform for evaluation of image quality in photon counting CT. The linearity of detector response was measured across a range of techniques (80 kVp, 0.03– 0.15 mAs), and a phantom consisting of simulated bone and soft tissue was used to evaluate the contrast to noise ratio (CNR) in CT reconstructions. The model was used to investigate limits in DQE as a function of imaging conditions and detector characteristics. Results: The signal response of the imaging system was highly linear with exposure (mR) across the operating range of the x‐ray source as predicted by the model, suggesting a lack of pulse pileup effects under conditions of interest. The soft‐tissue CNR ranged from 1.3 (at 2 mA) to 2.7 (at 10 mA), suggesting quantum‐limited performance and the potential advantage of zero electronic noise for low‐dose imaging. The model predicts zero‐frequency DQE ∼0.2–0.6 over the range 40–90 kVp and demonstrates an optimal range of signal threshold above the electronic noise but below the level of true counts. Conclusion: CSA modeling can be extended to include characteristics unique to PCDs and provide a basis for understanding the limits of imaging performance in photon counting CT. National Institutes of Health Grant No. 2R01‐CA‐112163‐02. Some authors affiliated with Phillips Healthcare.

Two major x‐ray‐based techniques used for medical imaging are digital radiography (DR) and computed tomography(CT). Most of their detectors integrate the intensity of x‐ray flux and output gray scale images or projections. Detectors with indirect detection type heavily weigh x‐ray photons with higher energy as they generate more lights. This results in suboptimal contrast of images because the contrast of different tissues reduces in general as the energy of photons increases. In the past few years, there have been strong reviving research interests in an old concept—the use of the photon energy—to improve the quality and accuracy of diagnosis. Recently, novel photon counting x‐ray detectors (PCXDs) with energy discrimination capabilities have been developed for x‐ray DR and CTimaging. These PCXDs counts the number of x‐ray photons within multiple energy windows. This allows us to improve the quality of the current gray scale images and the accuracy of the material decomposition. We will discuss the state‐of‐the‐art detector technologies and imaging methods unique to these PCXDs.