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.

Constrained one-step material decomposition reconstruction of head CT data from a silicon photon-counting prototype.

BACKGROUND: Spectral CT material decomposition provides quantitative information but is challenged by the instability of the inversion into basis materials. We have previously proposed the constrained One-Step Spectral CT Image Reconstruction (cOSSCIR) algorithm to stabilize the material decomposition inversion by directly estimating basis material images from spectral CT data. cOSSCIR was previously investigated on phantom data. PURPOSE: This study investigates the performance of cOSSCIR using head CT datasets acquired on a clinical photon-counting CT (PCCT) prototype. This is the first investigation of cOSSCIR for large-scale, anatomically complex, clinical PCCT data. The cOSSCIR decomposition is preceded by a spectrum estimation and nonlinear counts correction calibration step to address nonideal detector effects. METHODS: Head CT data were acquired on an early prototype clinical PCCT system using an edge-on silicon detector with eight energy bins. Calibration data of a step wedge phantom were also acquired and used to train a spectral model to account for the source spectrum and detector spectral response, and also to train a nonlinear counts correction model to account for pulse pileup effects. The cOSSCIR algorithm optimized the bone and adipose basis images directly from the photon counts data, while placing a grouped total variation (TV) constraint on the basis images. For comparison, basis images were also reconstructed by a two-step projection-domain approach of Maximum Likelihood Estimation (MLE) for decomposing basis sinograms, followed by filtered backprojection (MLE + FBP) or a TV minimization algorithm (MLE + TVmin ) to reconstruct basis images. We hypothesize that the cOSSCIR approach will provide a more stable inversion into basis images compared to two-step approaches. To investigate this hypothesis, the noise standard deviation in bone and soft-tissue regions of interest (ROIs) in the reconstructed images were compared between cOSSCIR and the two-step methods for a range of regularization constraint settings. RESULTS: cOSSCIR reduced the noise standard deviation in the basis images by a factor of two to six compared to that of MLE + TVmin , when both algorithms were constrained to produce images with the same TV. The cOSSCIR images demonstrated qualitatively improved spatial resolution and depiction of fine anatomical detail. The MLE + TVmin algorithm resulted in lower noise standard deviation than cOSSCIR for the virtual monoenergetic images (VMIs) at higher energy levels and constraint settings, while the cOSSCIR VMIs resulted in lower noise standard deviation at lower energy levels and overall higher qualitative spatial resolution. There were no statistically significant differences in the mean values within the bone region of images reconstructed by the studied algorithms. There were statistically significant differences in the mean values within the soft-tissue region of the reconstructed images, with cOSSCIR producing mean values closer to the expected values. CONCLUSIONS: The cOSSCIR algorithm, combined with our previously proposed spectral model estimation and nonlinear counts correction method, successfully estimated bone and adipose basis images from high resolution, large-scale patient data from a clinical PCCT prototype. The cOSSCIR basis images were able to depict fine anatomical details with a factor of two to six reduction in noise standard deviation compared to that of the MLE + TVmin two-step approach.

Feasibility of unconstrained three-material decomposition: imaging an excised human heart using a prototype silicon photon-counting CT detector.

RATIONALE AND OBJECTIVES: The purpose of this study was to evaluate the feasibility of unconstrained three-material decomposition in a human tissue specimen containing iodinated contrast agent, using an experimental multi-bin photon-counting silicon detector. It was further to evaluate potential added clinical value compared to a 1st-generation state-of-the-art dual-energy computed tomography system. MATERIALS AND METHODS: A prototype photon-counting silicon detector in a bench-top setup for x-ray tomographic imaging was calibrated using a multi-material calibration phantom. A heart with calcified plaque was obtained from a deceased patient, and the coronary arteries were injected with an iodinated contrast agent mixed with gelatin. The heart was imaged in the experimental setup and on a 1st-generation state-of-the-art dual-energy computed tomography system. Projection-based three-material decomposition without any constraints was performed with the photon-counting detector data, and the resulting images were compared with those obtained from the dual-energy system. RESULTS: The photon-counting detector images show better separation of iodine and calcium compared to the dual-energy images. Additional experiments confirmed that unbiased estimates of soft tissue, calcium, and iodine could be achieved without any constraints. CONCLUSION: The proposed experimental system could provide added clinical value compared to current dual-energy systems for imaging tasks where mix-up of iodine and calcium is an issue, and the anatomy is sufficiently small to allow iodine to be differentiated from calcium. Considering its previously shown count rate capability, these results show promise for future integration of this detector in a clinical CT scanner. KEY POINTS: • Spectral photon-counting detectors can solve some of the fundamental problems with conventional single-energy CT. • Dual-energy methods can be used to differentiate iodine and calcium, but to do so must rely on constraints, since solving for three unknowns with only two measurements is not possible. Photon-counting detectors can improve upon these methods by allowing unconstrained three-material decomposition. • A prototype photon-counting silicon detector with high count rate capability allows performing unconstrained three-material decomposition and qualitatively shows better differentiation of iodine and calcium than dual-energy CT.

Resolution characterization of a silicon-based, photon-counting computed tomography prototype capable of patient scanning.

Photon-counting detectors are expected to bring a range of improvements to patient imaging with x-ray computed tomography (CT). One is higher spatial resolution. We demonstrate the resolution obtained using a commercial CT scanner where the original energy-integrating detector has been replaced by a single-slice, silicon-based, photon-counting detector. This prototype constitutes the first full-field-of-view silicon-based CT scanner capable of patient scanning. First, the pixel response function and focal spot profile are measured and, combining the two, the system modulation transfer function is calculated. Second, the prototype is used to scan a resolution phantom and a skull phantom. The resolution images are compared to images from a state-of-the-art CT scanner. The comparison shows that for the prototype 19 lp / cm are detectable with the same clarity as 14 lp / cm on the reference scanner at equal dose and reconstruction grid, with more line pairs visible with increasing dose and decreasing image pixel size. The high spatial resolution remains evident in the anatomy of the skull phantom and is comparable to that of other photon-counting CT prototypes present in the literature. We conclude that the deep silicon-based detector used in our study could provide improved spatial resolution in patient imaging without increasing the x-ray dose.

Count statistics of nonparalyzable photon-counting detectors with nonzero pulse length.

PURPOSE: Photon-counting detectors are expected to be the next big step in the development of medical computed tomography (CT). Accurate modeling of the behavior of photon-counting detectors in both low and high count rate regimes is important for accurate image reconstruction and detector performance evaluations. The commonly used ideal nonparalyzable (delta pulse) model is built on crude assumptions that make it unsuitable for predicting the behavior of photon-counting detectors at high count rates. The aim of this work is to present an analytical count statistics model that better describes the behavior of photon-counting detectors with nonzero pulse length. METHODS: An analytical statistical count distribution model for nonparalyzable detectors with nonzero pulse length is derived using tools from statistical analysis. To validate the model, a nonparalyzable photon-counting detector is simulated using Monte Carlo methods and compared against. Image performance metrics are computed using the Fisher information metric and a comparison between the proposed model, approximations of the proposed model, and those made by the ideal nonparalyzable model is presented and analyzed. RESULTS: It is shown that the presented model agrees well with the results from the Monte Carlo simulation and is stable for varying x-ray beam qualities. It is also shown that a simple Gaussian approximation of the distribution can be used to accurately model the behavior and performance of nonparalyzable detectors with nonzero pulse length. Furthermore, the comparison of performance metrics show that the proposed model predicts a very different behavior than the ideal nonparalyzable detector model, suggesting that the proposed model can fill an important gap in the understanding of pileup effects. CONCLUSIONS: An analytical model for the count statistics of a nonparalyzable photon-counting detector with nonzero pulse length is presented. The model agrees well with results obtained from Monte Carlo simulations and can be used to improve, speed up and simplify modeling of photon-counting detectors.

Bias-variance tradeoff in anticorrelated noise reduction for spectral CT.

PURPOSE: In spectral CT, basis material decomposition is commonly used to generate a set of basis images showing the material composition at each point in the field of view. The noise in these images typically contains anticorrelations between the different basis images, which leads to increased noise in each basis image. These anticorrelations can be removed by changing the basis functions used in the material decomposition, but the resulting basis images can then no longer be used for quantitative measurements. Recent studies have demonstrated that reconstruction methods which take the anticorrelations into account give reduced noise in the reconstructed image. The purpose of this work is to analyze an analytically solvable denoising model problem and investigate its effect on the noise level and bias in the image as a function of spatial frequency. METHOD: A denoising problem with a quadratic regularization term is studied as a mathematically tractable model for such a reconstruction method. An analytic formula for the resulting image in the spatial frequency domain is presented, and this formula is applied to a simple mathematical phantom consisting of an iodinated contrast agent insert embedded in soft tissue. We study the effect of the denoising on the image in terms of its transfer function and the visual appearance, the noise power spectrum and the Fourier component correlation coefficient of the resulting image, and compare the result to a denoising problem which does not model the anticorrelations in the image. RESULTS: Including the anticorrelations in the noise model of the denoising method gives 3-40% lower noise standard deviation in the soft-tissue image while leaving the iodine standard deviation nearly unchanged (0-1% difference). It also gives a sharper edge-spread function. The studied denoising method preserves the noise level and the anticorrelated structure at low spatial frequencies but suppresses the noise and removes the anticorrelations at higher spatial frequencies. Cross-talk between images gives rise to artifacts at high spatial frequencies. CONCLUSIONS: Modeling anticorrelations in a denoising problem can decrease the noise level in the basis images by removing anticorrelations at high spatial frequencies while leaving low spatial frequencies unchanged. In this way, basis image cross-talk does not lead to low spatial frequency bias but it may cause artifacts at edges in the image. This theoretical insight will be useful for researchers analyzing and designing reconstruction algorithms for spectral CT.