Spatio-energetic cross-talk in photon counting detectors: Numerical detector model (PcTK) and workflow for CT image quality assessment

Evaluating spectral performance for quantitative contrast-enhanced breast CT with a GaAs based photon counting detector: a simulation approach

Quantitative contrast-enhanced breast computed tomography (CT) has the potential to improve the diagnosis and management of breast cancer. Traditional CT methods using energy-integrated detectors and dual-exposure images with different incident spectra for material discrimination can increase patient radiation dose and be susceptible to motion artifacts and spectral resolution loss. Photon Counting Detectors (PCDs) offer a promising alternative approach, enabling acquisition of multiple energy levels in a single exposure and potentially better energy resolution. Gallium arsenide (GaAs) is particularly promising for breast PCD-CT due to its high quantum efficiency and reduction of fluorescence x-rays escaping the pixel within the breast imaging energy range. In this study, the spectral performance of a GaAs PCD for quantitative iodine contrast-enhanced breast CT was evaluated. A GaAs detector with a pixel size of 100μm, a thickness of 500μm was simulated. Simulations were performed using cylindrical phantoms of varying diameters (10 cm, 12 cm, and 16 cm) with different concentrations and locations of iodine inserts, using incident spectra of 50, 55, and 60 kVp with 2 mm of added aluminum filtration and and a mean glandular dose of 10 mGy. We accounted for the effects of beam hardening and energy detector response using TIGRE CT open-source software and the publicly available Photon Counting Toolkit (PcTK). Material-specific images of the breast phantom were produced using both projection and image-based material decomposition methods, and iodine component images were used to estimate iodine intake. Accuracy and precision of the proposed methods for estimating iodine concentration in breast CT images were assessed for different material decomposition methods, incident spectra, and breast phantom thicknesses. The results showed that both the beam hardening effect and imperfection in the detector response had a significant impact on performance in terms of Root Mean Squared Error (RMSE), precision, and accuracy of estimating iodine intake in the breast. Furthermore, the study demonstrated the effectiveness of both material decomposition methods in making accurate and precise iodine concentration predictions using a GaAs-based photon counting breast CT system, with better performance when applying the projection-based material decomposition approach. The study highlights the potential of GaAs-based photon counting breast CT systems as viable alternatives to traditional imaging methods in terms of material decomposition and iodine concentration estimation, and proposes phantoms and figures of merit to assess their performance.

Multivariate signal-to-noise ratio as a metric for characterizing spectral computed tomography

Objective.With the introduction of spectral CT techniques into the clinic, the imaging capacities of CT were expanded to multiple energy levels. Due to a variety of factors, the acquired signal in spectral CT datasets is shared between these images. Conventional image quality metrics assume independence between images which is not preserved within spectral CT datasets, limiting their utility for characterizing energy selective images. The purpose of this work was to develop a metrology to characterize energy selective images by incorporating the shared information between images within a spectral CT dataset.Approach.The signal-to-noise ratio (SNR) was extended into a multivariate space where each image within a spectral CT dataset was treated as a separate information channel. The general definition was applied to the specific case of contrast to define a multivariate contrast-to-noise ratio (CNR). The matrix contained two types of terms: a conventional CNR term which characterized image quality within each image in the spectral CT dataset and covariance weighted CNR (Covar-CNR) which characterized the contrast in each image relative to the covariance between images. Experimental data from an investigational photon-counting CT scanner was used to demonstrate the insight of this metrology. A cylindrical water phantom containing vials of iodine and gadolinium (2, 4, and 8 mg ml-1) was imaged under conditions of variable tube current, tube voltage, and energy threshold. Two image series (threshold and bin images) containing two images each were defined based upon the contribution of photons to reconstructed images. Analysis of variance (ANOVA) was calculated between CNR terms and image acquisition variables. A multivariate regression was then fitted to experimental data.Main Results.Image type had a major difference on how Covar-CNR values were distributed. Bin images had a slightly higher mean and wider standard deviation (Covar-CNRlo: 3.38 ±17.25, Covar-CNRhi: 5.77 ± 30.64) compared to threshold images (Covar-CNRlo: 2.08 ±1.89, Covar-CNRhi: 3.45 ± 2.49) across all conditions. ANOVA found that each acquisition variable had a significant relationship with both Covar-CNR terms. The multivariate regression model suggested that material concentration had the largest impact on all CNR terms.Signficance.In this work, we described a theoretical framework to extend the SNR to a multivariate form that is able to characterize images independently and also provide insight regarding the relationship between images. Experimental data was used to demonstrate the insight that this metrology provides about image formation factors in spectral CT.

The effects of intra-detector Compton scatter on low-frequency DQE for photon-counting CT using edge-on-irradiated silicon detectors

BACKGROUND

Edge-on-irradiated silicon detectors are currently being investigated for use in full-body photon-counting computed tomography (CT) applications. The low atomic number of silicon leads to a significant number of incident photons being Compton scattered in the detector, depositing a part of their energy and potentially being counted multiple times. Even though the physics of Compton scatter is well established, the effects of Compton interactions in the detector on image quality for an edge-on-irradiated silicon detector have still not been thoroughly investigated.

PURPOSE

To investigate and explain effects of Compton scatter on low-frequency detective quantum efficiency (DQE) for photon-counting CT using edge-on-irradiated silicon detectors.

METHODS

We extend an existing Monte Carlo model of an edge-on-irradiated silicon detector with 60 mm active absorption depth, previously used to evaluate spatial-frequency-based performance, to develop projection and image domain performance metrics for pure density and pure spectral imaging tasks with 30 and 40 cm water backgrounds. We show that the lowest energy threshold of the detector can be used as an effective discriminator of primary counts and cross-talk caused by Compton scatter. We study the developed metrics as functions of the lowest threshold energy for root-mean-square electronic noise levels of 0.8, 1.6, and 3.2 keV, where the intermediate level 1.6 keV corresponds to the noise level previously measured on a single sensor element in isolation. We also compare the performance of a modeled detector with 8, 4, and 2 optimized energy bins to a detector with 1-keV-wide bins.

RESULTS

In terms of low-frequency DQE for density imaging, there is a tradeoff between using a threshold low enough to capture Compton interactions and avoiding electronic noise counts. For 30 cm water phantom, 4 energy bins, and a root-mean-square electronic noise of 0.8, 1.6, and 3.2 keV, it is optimal to put the lowest energy threshold at 3, 6, and 1 keV, which gives optimal projection-domain DQEs of 0.64, 0.59, and 0.52, respectively. Low-frequency DQE for spectral imaging also benefits from measuring Compton interactions with respective optimal thresholds of 12, 12, and 13 keV. No large dependence on background thickness was observed. For the intermediate noise level (1.6 keV), increasing the lowest threshold from 5 to 35 keV increases the variance in a iodine basis image by 60%-62% (30 cm phantom) and 67%-69% (40 cm phantom), with 8 bins. Both spectral and density DQE are adversely affected by increasing the electronic noise level. Image-domain DQE exhibits similar qualitative behavior as projection-domain DQE.

CONCLUSIONS

Compton interactions contribute significantly to the density imaging performance of edge-on-irradiated silicon detectors. With the studied detector topology, the benefit of counting primary Compton interactions outweighs the penalty of multiple counting at all lowest threshold energies. Compton interactions also contribute significantly to the spectral imaging performance for measured energies above 10 keV.

Development of a separability index for task specific characterization of spectral computed tomography

PURPOSE

In this work, we define a signal detection based metrology to characterize the separability of two different multi-dimensional signals in spectral CT acquisitions.

METHOD

Signal response was modelled as a random process with a deterministic signal and stochastic noise component. A linear Hotelling observer was used to estimate a scalar test statistic distribution that predicts the likelihood of an intensity value belonging to a signal. Two distributions were estimated for two materials of interest and used to derive two metrics separability: a separability index (s') and the area under the curve of the test statistic distributions. Experimental and simulated data of photon-counting CT scanners were used to evaluate each metric. Experimentally, vials of iodine and gadolinium (2, 4, 8 mg/mL) were scanned at multiple tube voltages, tube currents and energy thresholds. Additionally, a simulated dataset with low tube current (10-150 mAs) and material concentrations (0.25-4 mg/mL) was generated.

RESULTS

Experimental data showed that conditions favorable for low noise and expression of k-edge signal produced the highest separability. Material concentration had the greatest impact on separability. The simulated data showed that under more difficult separation conditions, difference in material concentration still had the greatest impact on separability.

CONCLUSION

The results demonstrate the utility of a task specific metrology to measure the overlap in signal between different materials in spectral CT. Using experimental and simulated data, the separability index was shown to describe the relationship between image formation factors and the signal responses of material.

Possible improvements in effective fill factor using X-ray fluorescent interpixel reflectors

BACKGROUND

The spatial resolution of energy-integrating diagnostic CT scanners is limited by interpixel reflectors on the detector, which optically isolate pixels but create dead space. Because the width of the reflector cannot easily be decreased, fill factor diminishes as resolution increases.

PURPOSE

We propose loading (or mixing) a high-Z element into the reflectors, causing the reflectors to be X-ray fluorescent. Re-emitted characteristic X-rays could be detected in adjacent pixels, increasing the effective fill factor and compensating for fill factor loss with higher-resolution detectors. The purpose of this work is to understand the physical principles of this approach and to analyze its effectiveness using Monte Carlo simulations.

METHODS

Detector pixels were modeled using the GEANT4 Monte Carlo package. The width of the reflector was kept constant at 0.1 mm throughout, and we considered pixel pitches between 0.5 and 1 mm. The pixelated scintillator material was gadolinium oxysulfide, 3 mm thick. The baseline reflector material was chosen to be acrylic, and varying concentrations of a high-Z element were loaded into the material. We assumed that the optical characteristics of pixels were ideal (no absorption within pixels, perfect reflection at boundaries). The detector was irradiated uniformly with 10,000 X-ray photons to estimate its spectral response. The figure of merit was the variance of the detector signal at zero frequency normalized to that of an ideal single-bin photon-counting detector with 100% fill factor. Sensitivity analyses were conducted to understand the effect of varying the high-Z element concentration and the spectrum.

RESULTS

Initial simulations suggested that a k-edge near 50 keV would be ideal. Gd was therefore selected as the high-Z material. The relative variances for a conventional energy integrating detector without Gd at 1 mm pixel pitch (81% fill factor) and 0.5 mm pixel pitch (64% fill factor) were 1.38 and 1.74, compared to 1.00 for an ideal photon counting detector, implying a 26% variance penalty for 0.5 mm pitch. When 1 g/cm3 Gd was loaded into the interpixel reflector, the relative variance improved to 1.27 and 1.43, respectively, implying that the variance penalty for including Gd together with 0.5 mm pitch is only 4%. Performance was nearly maximized at 1.0 g/cm3 of Gd, but a concentration of 0.5 g/cm3 of Gd showed most of the benefit. Improvements depend weakly on kV, with lower kV associated with higher improvements. An external anti-scatter grid was not modeled in our simulations and would reduce the expected benefit, depending greatly on the pitch and dimensionality of the anti-scatter grid.

CONCLUSIONS

The losses in fill factor associated with smaller pixel pitch can be reduced if Gd or a similar element could be loaded into the interpixel reflector. These improvements in noise efficiency are yet to be verified experimentally.

Improving model-data mismatch for photon-counting detector model using global and local model parameters

BACKGROUND

An energy-discriminating capability of a photon counting detector (PCD) can provide many clinical advantages, but several factors, such as charge sharing (CS) and pulse pileup (PP), degrade the capability by distorting the measured x-ray spectrum. To fully exploit the merits of PCDs, it is important to characterize the output of PCDs. Previously proposed PCD output models showed decent agreement with physical PCDs; however, there were still scopes to be improved: a global model-data mismatch and pixel-to-pixel variations.

PURPOSES

In this study, we improve a PCD model by using count-rate-dependent model parameters to address the issues and evaluate agreement against physical PCDs.

METHODS

The proposed model is based on the cascaded model, and we made model parameters condition-dependent and pixel-specific to deal with the global model-data mismatch and the pixel-to-pixel variation. The parameters are determined by a procedure for model parameter estimation with data acquired from different thicknesses of water or aluminum at different x-ray tube currents. To analyze the effects of having proposed model parameters, we compared three setups of our model: a model with default parameters, a model with global parameters, and a model with global-and-local parameters. For experimental validation, we used CdZnTe-based PCDs, and assessed the performance of the models by calculating the mean absolute percentage errors (MAPEs) between the model outputs and the actual measurements from low count-rates to high count-rates, which have deadtime losses of up to 24%.

RESULTS

The outputs of the proposed model visually matched well with the PCD measurements for all test data. For the test data, the MAPEs averaged over all the bins were 49.2-51.1% for a model with default parameters, 8.0-9.8% for a model with the global parameters, and 1.2-2.7% for a model with the global-and-local parameters.

CONCLUSION

The proposed model can estimate the outputs of physical PCDs with high accuracy from low to high count-rates. We expect that our model will be actively utilized in applications where the pixel-by-pixel accuracy of a PCD model is important.

Deep-silicon photon-counting x-ray projection denoising through reinforcement learning

BACKGROUND

In recent years, deep reinforcement learning (RL) has been applied to various medical tasks and produced encouraging results.

OBJECTIVE

In this paper, we demonstrate the feasibility of deep RL for denoising simulated deep-silicon photon-counting CT (PCCT) data in both full and interior scan modes. PCCT offers higher spatial and spectral resolution than conventional CT, requiring advanced denoising methods to suppress noise increase.

METHODS

In this work, we apply a dueling double deep Q network (DDDQN) to denoise PCCT data for maximum contrast-to-noise ratio (CNR) and a multi-agent approach to handle data non-stationarity.

RESULTS

Using our method, we obtained significant image quality improvement for single-channel scans and consistent improvement for all three channels of multichannel scans. For the single-channel interior scans, the PSNR (dB) and SSIM increased from 33.4078 and 0.9165 to 37.4167 and 0.9790 respectively. For the multichannel interior scans, the channel-wise PSNR (dB) increased from 31.2348, 30.7114, and 30.4667 to 31.6182, 30.9783, and 30.8427 respectively. Similarly, the SSIM improved from 0.9415, 0.9445, and 0.9336 to 0.9504, 0.9493, and 0.0326 respectively.

CONCLUSIONS

Our results show that the RL approach improves image quality effectively, efficiently, and consistently across multiple spectral channels and has great potential in clinical applications.

Dual-Energy Computed Tomography to Photon Counting Computed Tomography: Emerging Technological Innovations

Computed tomography (CT) has seen remarkable developments in the past several decades, radically transforming the role of imaging in day-to-day clinical practice. Dual-energy CT (DECT), an exciting innovation introduced in the early part of this century, has widened the scope of CT, opening new opportunities due to its ability to provide superior tissue characterization. The introduction of photon-counting CT (PCCT) heralds a paradigm shift in CT scanner technology representing another significant milestone in CT innovation. PCCT offers several advantages over DECT, such as improved spectral resolution, enhanced tissue characterization, reduced image artifacts, and improved image quality.

Inclusion of a GaAs detector model in the Photon Counting Toolkit software for the study of breast imaging systems

We present an upgraded version of the Photon Counting Toolkit (PcTK), a freely available by request MATLAB tool for the simulation of semiconductor-based photon counting detectors (PCD), which has been extended and validated to account for gallium arsenide (GaAs)-based PCD(s). The modified PcTK version was validated by performing simulations and acquiring experimental data for three different cases. The LAMBDA 60 K module planar detector (X-Spectrum GmbH, Germany) based on the Medipix3 ASIC technology was used in all cases. This detector has a 500-μm thick GaAs sensor and a 256 × 256-pixel array with 55 μm pixel size. The first validation was a comparison between simulated and measured spectra from a 109Cd radionuclide source. In the second validation study, experimental measurements and simulations of mammography spectra were generated to observe the performance of the GaAs version of the PcTK with polychromatic radiation used in conventional x-ray imaging systems. The third validation study used single event analysis to validate the spatio-energetic model of the extended PcTK version. Overall, the software provided a good agreement between simulated and experimental data, validating the accuracy of the GaAs model. The software could be an attractive tool for accurate simulation of breast imaging modalities relying on photon counting detectors and therefore could assist in their characterization and optimization.

Model-based pulse pileup and charge sharing compensation for photon counting detectors: A simulation study

Purpose

We aim at developing a model‐based algorithm that compensates for the effect of both pulse pileup (PP) and charge sharing (CS) and evaluates the performance using computer simulations.

Methods

The proposed PCP algorithm for PP and CS compensation uses cascaded models for CS and PP we previously developed, maximizes Poisson log‐likelihood, and uses an efficient three‐step exhaustive search. For comparison, we also developed an LCP algorithm that combines models for a loss of counts (LCs) and CS. Two types of computer simulations, slab‐ and computed tomography (CT)‐based, were performed to assess the performance of both PCP and LCP with 200 and 800 mA, (300 µm)² × 1.6‐mm cadmium telluride detector, and a dead‐time of 23 ns. A slab‐based assessment used a pair of adipose and iodine with different thicknesses, attenuated X‐rays, and assessed the bias and noise of the outputs from one detector pixel; a CT‐based assessment simulated a chest/cardiac scan and a head‐and‐neck scan using 3D phantom and noisy cone‐beam projections.

Results

With the slab simulation, the PCP had little or no biases when the expected counts were sufficiently large, even though a probability of count loss (PCL) due to dead‐time loss or PP was as high as 0.8. In contrast, the LCP had significant biases (>±2 cm of adipose) when the PCL was higher than 0.15. Biases were present with both PCP and LCP when the expected counts were less than 10–120 per datum, which was attributed to the fact that the maximum likelihood did not approach the asymptote. The noise of PCP was within 8% from the Cramér–Rao lower bounds for most cases when no significant bias was present. The two CT studies essentially agreed with the slab simulation study. PCP had little or no biases in the estimated basis line integrals, reconstructed basis density maps, and synthesized monoenergetic CT images. But the LCP had significant biases in basis line integrals when X‐ray beams passed through lungs and near the body and neck contours, where the PCLs were above 0.15. As a consequence, basis density maps and monoenergetic CT images obtained by LCP had biases throughout the imaged space.

Conclusion

We have developed the PCP algorithm that uses the PP–CS model. When the expected counts are more than 10–120 per datum, the PCP algorithm is statistically efficient and successfully compensates for the effect of the spectral distortion due to both PP and CS providing little or no biases in basis line integrals, basis density maps, and monoenergetic CT images regardless of count‐rates. In contrast, the LCP algorithm, which models an LC due to pileup, produces severe biases when incident count‐rates are high and the PCL is 0.15 or higher.

Ultra-Low-Dose Spectral CT Based on a Multi-level Wavelet Convolutional Neural Network

Spectral computed tomography (CT) based on a photon-counting detector (PCD) is a promising technique with the potential to improve lesion detection, tissue characterization, and material decomposition. PCD-based scanners have several technical issues including operation in the step-and-scan mode and long data acquisition time. One straightforward solution to these issues is to reduce the number of projection views. However, if the projection data are under-sampled or noisy, it would be challenging to produce a correct solution without precise prior information. Recently, deep-learning approaches have demonstrated impressive performance for under-sampled CT reconstruction. In this work, the authors present a multilevel wavelet convolutional neural network (MWCNN) to address the limitations of PCD-based scanners. Data properties of the proposed method in under-sampled spectral CT are analyzed with respect to the proposed deep-running-network-based image reconstruction using two measures: sampling density and data incoherence. This work presents the proposed method and four different methods to restore sparse sampling. We investigate and compare these methods through a simulation and real experiments. In addition, data properties are quantitatively analyzed and compared for the effect of sparse sampling on the image quality. Our results indicate that both sampling density and data incoherence affect the image quality in the studied methods. Among the different methods, the proposed MWCNN shows promising results. Our method shows the highest performance in terms of various evaluation parameters such as the structural similarity, root mean square error, and resolution. Based on the results of imaging and quantitative evaluation, this study confirms that the proposed deep-running network structure shows excellent image reconstruction in sparse-view PCD-based CT. These results demonstrate the feasibility of sparse-view PCD-based CT using the MWCNN. The advantage of sparse view CT is that it can significantly reduce the radiation dose and obtain images with several energy bands by fusing PCDs. These results indicate that the MWCNN possesses great potential for sparse-view PCD-based CT.

Assessment of multi-energy inter-pixel coincidence counters for photon-counting detectors at the presence of charge sharing and pulse pileup: A simulation study

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 in 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 1000 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 provide better nCRLBs than the conventional PCD does only when count rates are very low.

Improving digital charge sharing compensation in photon counting detectors with a low-threshold comparator

PURPOSE

Charge sharing is a major non-ideality in photon counting detectors (PCDs) and can increase variance in material decomposition images. Analog charge summing (ACS) is an effective mechanism for charge sharing compensation (CSC), but is complex to implement and may limit the maximum count rate of the PCD. Digital CSC mechanisms such as digital count summing (DCS) may be simpler to implement; however, earlier simulation studies suggest that digital CSC only provides half the benefit of ACS. We propose including an additional low-threshold comparator (LTC) underneath the noise floor of the PCD to improve the effectiveness of digital CSC.

METHODS

We simulated a PCD with four or eight equally spaced energy bins. X-ray photons arrived on the PCD following a Poisson distribution, and charge was allocated to PCD pixels following Monte Carlo techniques. Gaussian electronic noise was added with standard deviation of 2 keV and the signals were processed with four CSC schemes: no CSC, ACS, DCS, and DCS with LTC. The energy bins were placed from 25 to 100 keV at 25 keV intervals (for four bins) or from 25 to 112.5 keV at 12.5 keV intervals (for eight bins), and the LTC threshold was placed at 8 keV in both cases. The binned counts were transformed into estimates of water and iodine material thickness using a linear estimator that was fitted to the data. Our simulations were performed in the low-flux limit without any pileup, assuming a 120 kVp spectrum, 25 cm water object, and 0.3 mm PCD pixel size.

RESULTS

All CSC schemes decreased variance in basis material decomposition. In the four-bin PCD, the relative dose efficiencies (inverse of the variance) for iodine material decomposition were 1.0, 2.4, 3.2, and 4.3 for a PCD without CSC, DCS without LTC, DCS with LTC, and ACS, respectively. In the eight-bin PCD, the relative dose efficiencies were 1.1, 2.5, 3.1, and 4.8, respectively. In a sensitivity analysis, electronic noise had a stronger deleterious effect on ACS than DCS. In simulated visual images, DCS and ACS improved high frequency contrast in material decomposition images.

CONCLUSIONS

Introducing an LTC may reduce the performance differential between DCS and ACS. These findings have been derived from simulation studies only and have not been validated experimentally.

Advances in micro-CT imaging of small animals

PURPOSE

Micron-scale computed tomography (micro-CT) imaging is a ubiquitous, cost-effective, and non-invasive three-dimensional imaging modality. We review recent developments and applications of micro-CT for preclinical research.

METHODS

Based on a comprehensive review of recent micro-CT literature, we summarize features of state-of-the-art hardware and ongoing challenges and promising research directions in the field.

RESULTS

Representative features of commercially available micro-CT scanners and some new applications for both in vivo and ex vivo imaging are described. New advancements include spectral scanning using dual-energy micro-CT based on energy-integrating detectors or a new generation of photon-counting x-ray detectors (PCDs). Beyond two-material discrimination, PCDs enable quantitative differentiation of intrinsic tissues from one or more extrinsic contrast agents. When these extrinsic contrast agents are incorporated into a nanoparticle platform (e.g. liposomes), novel micro-CT imaging applications are possible such as combined therapy and diagnostic imaging in the field of cancer theranostics. Another major area of research in micro-CT is in x-ray phase contrast (XPC) imaging. XPC imaging opens CT to many new imaging applications because phase changes are more sensitive to density variations in soft tissues than standard absorption imaging. We further review the impact of deep learning on micro-CT. We feature several recent works which have successfully applied deep learning to micro-CT data, and we outline several challenges specific to micro-CT.

CONCLUSIONS

All of these advancements establish micro-CT imaging at the forefront of preclinical research, able to provide anatomical, functional, and even molecular information while serving as a testbench for translational research.

A data-driven maximum likelihood classification for nanoparticle agent identification in photon-counting CT

The nanoparticle agent, combined with a targeting factor reacting with lesions, enables specific CT imaging. Thus, the identification of the nanoparticle agents has the potential to improve clinical diagnosis. Thanks to the energy sensitivity of the photon-counting detector (PCD), it can exploit the K-edge of the nanoparticle agents in the clinical x-ray energy range to identify the agents. In this paper, we propose a novel data-driven approach for nanoparticle agent identification using the PCD. We generate two sets of training data consisting of PCD measurements from calibration phantoms, one in the presence of nanoparticle agent and the other in the absence of the agent. For a given sinogram of PCD counts, the proposed method calculates the normalized log-likelihood sinogram for each class (class 1: with the agent, class 2: without the agent) using theKnearest neighbors (KNN) estimator, backproject the sinograms, and compare the backprojection images to identify the agent. We also proved that the proposed algorithm is equivalent to the maximum likelihood-based classification. We studied the robustness of dose reduction with gold nanoparticles as the K-edge contrast media and demonstrated that the proposed method identifies targets with different concentrations of the agents without background noise.

Spectral Photon Counting CT: Imaging Algorithms and Performance Assessment

Photon counting x-ray detectors (PCDs) with spectral capabilities have the potential to revolutionize computed tomography (CT) for medical imaging. The ideal PCD provides accurate energy information for each incident x-ray, and at high spatial resolution. This information enables material-specific imaging, enhanced radiation dose efficiency, and improved spatial resolution in CT images. In practice, PCDs are affected by non-idealities, including limited energy resolution, pulse pileup, and cross talk due to charge sharing, K-fluorescence, and Compton scattering. In order to maximize their performance, PCDs must be carefully designed to reduce these effects and then later account for them during correction and post-acquisition steps. This review article examines algorithms for using PCDs in spectral CT applications, including how non-idealities impact image quality. Performance assessment metrics that account for spatial resolution and noise such as the detective quantum efficiency (DQE) can be used to compare different PCD designs, as well as compare PCDs with conventional energy integrating detectors (EIDs). These methods play an important role in enhancing spectral CT images and assessing the overall performance of PCDs.

Photon Counting CT: Clinical Applications and Future Developments

The use of a photon counting detector in CT (PCD CT) is currently the subject of intense investigation and development. In this review article, we will describe potential clinical applications of this technology with a particular focus on the experience of our own institution with a prototype PCD CT scanner. PCDs have three primary advantages over conventional, energy integrating detectors (EIDs): they provide spectral information without need for a dedicated dual energy protocol; they are immune to electronic noise; and they can be made very high resolution without significant compromises to quantum efficiency. These advantages translate into several clinical applications. Metal artifacts, beam hardening artifacts, and noise streaks from photon starvation can be better mitigated using PCD CT. Certain incidental findings can be better characterized using the spectral information from PCD CT. High-contrast, high-resolution structures such as the temporal bone can be better visualized using PCD CT and at greatly reduced dose. We also discuss new possibilities on the horizon, including new contrast agents, and how anticipated improvements in PCD CT will translate to performance in these applications.

A novel algorithm for extracting soft-tissue and bone images measured using a photon-counting type X-ray imaging detector with the help of effective atomic number analysis

Most of the objects targeted for X-ray examination are composed of soft-tissue and bone. We aimed to develop an algorithm for generating X-ray images which can give quantitative information of soft-tissue and bone using an energy-resolving photon-counting type imaging detector. We used polychromatic X-rays for analysis in which both the beam hardening effect and detector response were properly corrected and then succeeded in virtually treating the amount of measured X-ray attenuation as if it were measured using monochromatic X-rays.

An x-ray crosstalk correction method using FCNN for a novel energy resolving scheme in spectral CT

Spectral computed tomography has great potential for multi-energy imaging and anti-artifacts. The complete absorption-based energy resolving scheme of x-rays has been used for the integrity of detected information. However, this scheme is limited by the fact that the detector pixel thickness is high and fixed. Here, an energy resolving scheme is proposed using the crosstalk correction method for the incomplete absorption detection of x-rays. A fully connected neural network (FCNN)-based method was used to correct the difference caused by internal x-ray crosstalk of the edge-on detector. The energy and spatial features of the data which is collected in layers were combined to establish the mapping between the ideal data and the data with crosstalk at the pre-processing stage. Thereafter, to reconstruct the stable and highly accurate energy-resolving equations, the layers with low relative energy difference were selected and grouped together to reduce the accumulation difference. The experiment results demonstrate the feasibility of this energy resolving scheme. The differences caused by crosstalk can be suppressed through the proposed FCNN-based method. The resolving accuracy can be further improved by grouping more layers at forward positions in the pixel. Moreover, this improvement can be observed in the reconstructed images with reduced artifacts and improved quality.

Anomalous edge response of cadmium telluride-based photon counting detectors jointly caused by high-flux radiation and inter-pixel communication

This work reports an edge enhancing effect experimentally observed in cadmium telluride (CdTe)-based photon counting detector (PCD) systems operated under the charge summing (CS) mode and irradiated by high-flux x-rays. Experimental measurements of the edge spread functions (ESFs) of a PCD system (100μm pixel size, 88 ns deadtime) were performed at different input flux levels from 4.5 × 105count per second (cps) mm-2to 1.5 × 109cps mm-2for the single pixel mode (SP) and the CS mode. A theoretical model that incorporates the impacts of inter-pixel communications and the arbitration process involved in the CS mode was developed to help explain the physical origin of the observed edge enhancing effect. Compared with the monotonically increasing ESF of the SP mode, the ESF of the CS mode measured at high-flux levels shows a peak at an intermediate location (50μm from the edge). The peak became more pronounced with increasing flux levels. The theoretically calculated ESFs agreed well with experimental results with relative errors less than 5% at all flux levels and tested. These results indicate that the anomalous edge enhancing effect is jointly caused by the pileup effect and the CS circuit that introduces negative correlations between adjacent pixels. When the input flux is high enough to deliver photons to multiple adjacent pixels within the same deadtime period, the CS mode may treat the coincident x-rays as shared charges and thus introduce count losses in addition to the well-known pileup count loss. When a high contrast object partially blocks certain pixels from x-rays, the adjacent unblocked pixels have an increased probability of registering counts as a result of the negative correlation. This leads to a peak on the ESF at a pixel-to-edge distance half of the pixel pitch.

Photon-counting x-ray detectors for CT

The introduction of photon-counting detectors is expected to be the next major breakthrough in clinical x-ray computed tomography (CT). During the last decade, there has been considerable research activity in the field of photon-counting CT, in terms of both hardware development and theoretical understanding of the factors affecting image quality. In this article, we review the recent progress in this field with the intent of highlighting the relationship between detector design considerations and the resulting image quality. We discuss detector design choices such as converter material, pixel size, and readout electronics design, and then elucidate their impact on detector performance in terms of dose efficiency, spatial resolution, and energy resolution. Furthermore, we give an overview of data processing, reconstruction methods and metrics of imaging performance; outline clinical applications; and discuss potential future developments.

Review of Technical Advancements and Clinical Applications of Photon-counting Computed Tomography in Imaging of the Thorax

Photon-counting computed tomography (CT) is a developing technology that has the potential to address some limitations of CT imaging and bring about improvements and potentially new applications to this field. Photon-counting detectors have a fundamentally different detection mechanism from conventional CT energy-integrating detectors that can improve dose efficiency, spatial resolution, and energy-discrimination capabilities. In the past decade, promising human studies have been reported in the literature that have demonstrated benefits of this relatively new technology for various clinical applications. In this review, we provide a succinct description of the photon-counting detector technology and its detection mechanism in comparison with energy-integrating detectors in a manner understandable for clinicians and radiologists, introduce benefits and some of the existing challenges present in this technology, and provide an overview of the current status and potential clinical applications of this technology in imaging of the thorax by providing example images acquired with an investigational whole-body photon-counting CT scanner.

Improving Paralysis Compensation in Photon Counting Detectors

Photon counting detectors (PCDs) are classically described as being either paralyzable or nonparalyzable. When the PCD is paralyzed, it is no longer sensitive to the detection of additional flux. A recent strategy in PCD design has been to compensate for detector paralysis by embedding specialized paralysis compensation electronics into the application-specific integrated circuit (ASIC). One such compensation mechanism is the pileup trigger, which places an additional energy bin at very high energy that is triggered only during pileup. Another compensation mechanism is the retrigger architecture, which converts a paralyzable PCD into a nonparalyzable PCD. We propose a third mechanism that modifies the retrigger architecture using dedicated secondary counters. We studied the incremental benefit of these three paralysis compensation mechanisms in simulation. We modeled the spectral response using Monte Carlo simulations and then estimated the variance in basis material decomposition of a single pixel using the Cramér-Rao lower bound (CRLB). In the absence of paralysis compensation, noise in basis material images shows sharp increases at moderate flux (near the characteristic count rate) due to contrast inversion and again at high flux. The pileup trigger reduces noise at high flux but does not eliminate contrast inversion. The retrigger architecture eliminates contrast inversion but does not reduce noise at high flux. Our proposed retrigger architecture with dedicated secondary counters reduce noise at both moderate and high flux.

Multi-energy computed tomography and material quantification: Current barriers and opportunities for advancement

Computed tomography (CT) technology has rapidly evolved since its introduction in the 1970s. It is a highly important diagnostic tool for clinicians as demonstrated by the significant increase in utilization over several decades. However, much of the effort to develop and advance CT applications has been focused on improving visual sensitivity and reducing radiation dose. In comparison to these areas, improvements in quantitative CT have lagged behind. While this could be a consequence of the technological limitations of conventional CT, advanced dual-energy CT (DECT) and photon-counting detector CT (PCD-CT) offer new opportunities for quantitation. Routine use of DECT is becoming more widely available and PCD-CT is rapidly developing. This review covers efforts to address an unmet need for improved quantitative imaging to better characterize disease, identify biomarkers, and evaluate therapeutic response, with an emphasis on multi-energy CT applications. The review will primarily discuss applications that have utilized quantitative metrics using both conventional and DECT, such as bone mineral density measurement, evaluation of renal lesions, and diagnosis of fatty liver disease. Other topics that will be discussed include efforts to improve quantitative CT volumetry and radiomics. Finally, we will address the use of quantitative CT to enhance image-guided techniques for surgery, radiotherapy and interventions and provide unique opportunities for development of new contrast agents.

Detective quantum efficiency of photon-counting CdTe and Si detectors for computed tomography: a simulation study

Purpose: Developing photon-counting CT detectors requires understanding the impact of parameters, such as converter material, thickness, and pixel size. We apply a linear-systems framework, incorporating spatial and energy resolution, to study realistic silicon (Si) and cadmium telluride (CdTe) detectors at a low count rate. Approach: We compared CdTe detector designs with 0.5 × 0.5    mm 2 and 0.225 × 0.225    mm 2 pixels and Si detector designs with 0.5 × 0.5    mm 2 pixels of 30 and 60 mm active thickness, with and without tungsten scatter blockers. Monte-Carlo simulations of photon transport were used together with Gaussian charge sharing models fitted to published data. Results: For detection in a 300-mm-thick object at 120 kVp, the 0.5- and 0.225-mm pixel CdTe systems have 28% to 41% and 5% to 29% higher detective quantum efficiency (DQE), respectively, than the 60-mm Si system with tungsten, whereas the corresponding numbers for two-material decomposition are 2% lower to 11% higher DQE and 31% to 54% lower DQE compared to Si. We also show that combining these detectors with dual-spectrum acquisition is beneficial. Conclusions: In the low-count-rate regime, CdTe detector systems outperform the Si systems for detection tasks, whereas silicon outperforms one or both of the CdTe systems for material decomposition.

Assessment of Multienergy Interpixel Coincidence Counters (MEICC) for Charge Sharing Correction or Compensation for Photon Counting Detectors With Boxcar Signals

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 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 charge sharing 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 charge sharing more signals than a PCD without charge sharing. In this paper, we propose to use spatially modulated boxcar signals for evaluating the performances for high spatial frequency tasks because they provide consistent signals regardless of the presence of absence of charge sharing. 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 Cramér-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-μm pixel were close to the current 450-μm PCD. We studied a combination of flat-field signals and N×N super-pixels, where the output of N×N pixels were added, using an MC simulation and a simple charge sharing counting model. The study showed that charge sharing had two opposing impacts on the conventional CT imaging-a negative impact with double-counting among N×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×N super-pixels such as N≥25 was suggested to approximate the zero-frequency detection quantum efficiency of PCD with charge sharing.

Multi-energy inter-pixel coincidence counters for charge sharing correction and compensation in photon counting detectors

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 Cramér-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.

Frequency-dependent signal and noise in spectroscopic x-ray imaging

Purpose

We present a new framework for theoretical analysis of the noise power spectrum (NPS) of photon‐counting x‐ray detectors, including simple photon‐counting detectors (SPCDs) and spectroscopic x‐ray detectors (SXDs), the latter of which use multiple energy thresholds to discriminate photon energies.

Methods

We show that the NPS of SPCDs and SXDs, including spatio‐energetic noise correlations, is determined by the joint probability density function (PDF) of deposited photon energies, which describes the probability of recording two photons of two different energies in two different elements following a single‐photon interaction. We present an analytic expression for this joint PDF and calculate the presampling and digital NPS of CdTe SPCDs and SXDs. We calibrate our charge sharing model using the energy response of a cadmium zinc telluride (CZT) spectroscopic x‐ray detector and compare theoretical results with Monte Carlo simulations.

Results

Our analysis shows that charge sharing increases pixel signal‐to‐noise ratio (SNR), but degrades the zero‐frequency signal‐to‐noise performance of SPCDs and SXDs. In all cases considered, this degradation was greater than 10%. Comparing the presampling NPS with the sampled NPS showed that degradation in zero‐frequency performance is due to zero‐frequency noise aliasing induced by charge sharing.

Conclusions

Noise performance, including spatial and energy correlations between elements and energy bins, are described by the joint PDF of deposited energies which provides a method of determining the photon‐counting NPS, including noise‐aliasing effects and spatio‐energetic effects in spectral imaging. Our approach enables separating noise due to x‐ray interactions from that associated with sampling, consistent with cascaded systems analysis of energy‐integrating systems. Our methods can be incorporated into task‐based assessment of image quality for the design and optimization of spectroscopic x‐ray detectors.

Coincidence Counters for Charge Sharing Compensation in Spectroscopic Photon Counting Detectors

The performance of X-ray photon counting detectors (PCDs), especially on spectral tasks, is compromised by charge sharing. Existing mechanisms to compensate for charge sharing, such as charge summing circuitry or larger pixel sizes, increase and aggravate pileup effects. We propose a new mechanism, the coincidence counting bin (CCB), which does not increase pileup and which has implementation similarities to existing energy bins. The CCB is triggered by coincident events in adjacent pixels and provides an estimate of the double counts arising from charge sharing. Unlike charge summing, the CCB does not directly restore corrupted events. Nonetheless, knowledge of the number of coincident counts can be used by the estimator to reduce noise. We simulated a PCD with and without the CCB using Monte Carlo simulations, modeling PCD pixels as instantaneous charge collectors and X-ray energy deposition as producing a Gaussian charge cloud with 75 micron FWHM, independent of energy. With typical operating conditions and at low flux (120 kVp, incident count rate 1% of characteristic count rate, 30 cm object thickness, five energy bins, pixel pitch of 300 microns), the CCB improved dose efficiency of iodine and water basis material decomposition by 70% and 50%, respectively. An improvement of 20% was also seen in an iodine CNR task. These improvements are attenuated as incident flux increases and show moderate dependence on filtration and pixel size. At high flux, the CCB does not provide useful information and is discarded by the estimator. The CCB may be an effective and practical mechanism for charge sharing compensation in PCDs.

Photon-counting cine-cardiac CT in the mouse

The maturation of photon-counting detector (PCD) technology promises to enhance routine CT imaging applications with high-fidelity spectral information. In this paper, we demonstrate the power of this synergy and our complementary reconstruction techniques, performing 4D, cardiac PCD-CT data acquisition and reconstruction in a mouse model of atherosclerosis, including calcified plaque. Specifically, in vivo cardiac micro-CT scans were performed in four ApoE knockout mice, following their development of calcified plaques. The scans were performed with a prototype PCD (DECTRIS, Ltd.) with 4 energy thresholds. Projections were sampled every 10 ms with a 10 ms exposure, allowing the reconstruction of 10 cardiac phases at each of 4 energies (40 total 3D volumes per mouse scan). Reconstruction was performed iteratively using the split Bregman method with constraints on spectral rank and spatio-temporal gradient sparsity. The reconstructed images represent the first in vivo, 4D PCD-CT data in a mouse model of atherosclerosis. Robust regularization during iterative reconstruction yields high-fidelity results: an 8-fold reduction in noise standard deviation for the highest energy threshold (relative to unregularized algebraic reconstruction), while absolute spectral bias measurements remain below 13 Hounsfield units across all energy thresholds and scans. Qualitatively, image domain material decomposition results show clear separation of iodinated contrast and soft tissue from calcified plaque in the in vivo data. Quantitatively, spatial, spectral, and temporal fidelity are verified through a water phantom scan and a realistic MOBY phantom simulation experiment: spatial resolution is robustly preserved by iterative reconstruction (10% MTF: 2.8–3.0 lp/mm), left-ventricle, cardiac functional metrics can be measured from iodine map segmentations with ~1% error, and small calcifications (615 μm) can be detected during slow moving phases of the cardiac cycle. Given these preliminary results, we believe that PCD technology will enhance dynamic CT imaging applications with high-fidelity spectral and material information.

Development of a scanner-specific simulation framework for photon-counting computed tomography

The aim of this study was to develop and validate a simulation platform that generates photon-counting CT images of voxelized phantoms with detailed modeling of manufacturer-specific components including the geometry and physics of the x-ray source, source filtrations, anti-scatter grids, and photon-counting detectors. The simulator generates projection images accounting for both primary and scattered photons using a computational phantom, scanner configuration, and imaging settings. Beam hardening artifacts are corrected using a spectrum and threshold dependent water correction algorithm. Physical and computational versions of a clinical phantom (ACR) were used for validation purposes. The physical phantom was imaged using a research prototype photon-counting CT (Siemens Healthcare) with standard (macro) mode, at four dose levels and with two energy thresholds. The computational phantom was imaged with the developed simulator with the same parameters and settings used in the actual acquisition. Images from both the real and simulated acquisitions were reconstructed using a reconstruction software (FreeCT). Primary image quality metrics such as noise magnitude, noise ratio, noise correlation coefficients, noise power spectrum, CT number, in-plane modulation transfer function, and slice sensitivity profiles were extracted from both real and simulated data and compared. The simulator was further evaluated for imaging contrast materials (bismuth, iodine, and gadolinium) at three concentration levels and six energy thresholds. Qualitatively, the simulated images showed similar appearance to the real ones. Quantitatively, the average relative error in image quality measurements were all less than 4% across all the measurements. The developed simulator will enable systematic optimization and evaluation of the emerging photon-counting computed tomography technology.

Multi-energy computed tomography reconstruction using a nonlocal spectral similarity model

Multi-energy computed tomography (MECT) is able to acquire simultaneous multi-energy measurements from one scan. In addition, it allows material differentiation and quantification effectively. However, due to the limited energy bin width, the number of photons detected in an energy-specific channel is smaller than that in traditional CT, which results in image quality degradation. To address this issue, in this work, we develop a statistical iterative reconstruction algorithm to acquire high-quality MECT images and high-accuracy material-specific images. Specifically, this algorithm fully incorporates redundant self-similarities within nonlocal regions in the MECT image at one bin and rich spectral similarities among MECT images at all bins. For simplicity, the presented algorithm is referred to as 'MECT-NSS'. Moreover, an efficient optimization algorithm is developed to solve the MECT-NSS objective function. Then, a comprehensive evaluation of parameter selection for the MECT-NSS algorithm is conducted. In the experiment, the datasets include images from three phantoms and one patient to validate and evaluate the MECT-NSS reconstruction performance. The qualitative and quantitative results demonstrate that the presented MECT-NSS can successfully yield better MECT image quality and more accurate material estimation than the competing algorithms.

Spatio-energetic cross-talk in photon counting detectors: N × N binning and sub-pixel masking

PURPOSE

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 × 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 × 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.

METHODS

We used a PCD cross-talk model (Photon counting toolkit, PcTK) and produced cross-talk data between 3 × 3 neighboring sub-pixels and calculated the mean, variance, and covariance of output-pixels with each of N × N binning scheme [4 × 4 binning, 2 × 2 binning, and 1 × 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

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 × 4 binning and 1 × 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 × 1 (900 μm)² binning, 2 × 2 (450 μm)² binning, and 4 × 4 (225 μm)² binning for a given masking method but the difference between each of them were typically 0.02-0.05.

CONCLUSION

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.

Effect of Spectral Degradation and Spatio-Energy Correlation in X-Ray PCD for Imaging

Charge sharing, scatter, and fluorescence events in a photon counting detector can result in counting of a single incident photon in multiple neighboring pixels, each at a fraction of the true energy. This causes energy distortion and correlation of data across energy bins in neighboring pixels (spatio-energy correlation), with the severity depending on the detector pixel size and detector material. If a "macro-pixel" is formed by combining the counts from multiple adjacent small pixels, it will exhibit correlations across its energy bins. Understanding these effects can be crucial for detector design and for model-based imaging applications. This paper investigates the impact of these effects in basis material and effective monoenergetic estimates using the Cramér-Rao Lower Bound. To do so, we derive a correlation model for the multi-counting events. CdTe detectors with grids of pixels with side length of $250~\mu \text{m}$ , $500~\mu \text{m}$ , and 1 mm were compared, with binning of $4\times4$ , $2\times2$ , and $1\times1$ pixels, respectively, to keep the same net 1 mm2 aperture constant. The same flux was applied to each. The mean and covariance matrix of measured photon counts were derived analytically using spatio-energy response functions precomputed from Monte Carlo simulations. Our results show that a 1 mm2 macro-pixel with $250\times 250\,\,\mu \text{m}^{\textsf {2}}$ sub-pixels shows 35% higher standard deviation than a single 1 mm2 pixel for material-specific imaging, while the penalty for effective monoenergetic imaging is <10% compared with a single 1 mm $^{\textsf {2}}$ pixel. Potential benefits of sub-pixels (higher spatial resolution and lower pulse pile-up effects) are important but were not investigated here.

Digital count summing vs analog charge summing for photon counting detectors: A performance simulation study

PURPOSE

Charge sharing is a significant problem for CdTe-based photon counting detectors (PCDs) and can cause high-energy photons to be misclassified as one or more low-energy events. Charge sharing is especially problematic in PCDs for CT because the high flux necessitates small pixels, which increase the magnitude of charge sharing. Analog charge summing (ACS) is a powerful solution to reduce spectral distortion arising from charge sharing but may be difficult to implement. We investigate correction of the signal after digitization by the comparator ("digital count summing"), which is only able to correct a subset of charge sharing events but may have implementation advantages. We compare and quantify the relative performance of digital and ACS in simulations.

METHODS

Transport of photons in CdTe was modeled using Monte Carlo simulations. Energy deposited in the CdTe substrate was converted to electrical charges of a predetermined shape, and all charges within the detector pixel are assumed to be perfectly collected. In ACS, the maximum charge received over any 2 × 2 block of pixels was grouped together prior to digitization. In digital count summing (DCS), the charge was digitized in each pixel, and subsequently, adjacent pixels that detected events grouped their charge to record a single, higher energy event. All simulations were performed at the limit of low flux (no pileup). The default tube voltage was 120 kVp, object thickness was 20 cm of water, pixel pitch was 250 μm, and charge cloud modeled as a Gaussian with σ = 40 μm. Variation of these parameters was examined in a sensitivity analysis.

RESULTS

Detectors that used no correction, DCS, and ACS misclassified 51%, 39%, and 15% of incident photons, respectively. For iodine basis material imaging, DCS exhibited 100% greater dose efficiency compared to uncorrected, and ACS exhibited an additional 111% greater dose efficiency compared to digital charge summing. For a nonspectral task, the dose efficiency improvement as estimated by improvement of zero-frequency detective quantum efficiency, DQE(0) was 10% for DCS compared to uncorrected and 10% for ACS compared to DCS. A sensitivity analysis showed that DCS generally achieved half the benefit of ACS over a range of conditions, although the benefit was markedly less if the charge cloud was instead modeled as a small sphere.

CONCLUSIONS

Summing of counts after digitization may be a simpler alternative to summing of charge prior to digitization due to the relative complexity of analog circuit design. Over most conditions studied, it provides roughly half the benefit of ACS and may offer certain implementation advantages.