For large cone angle multi-detector CT (MDCT), the scattered radiation remains a challenging problem as it is part of the physics process in X-ray interaction. For a photon counting CT system, the scattered radiation has more profound impact to the system performance, as the scattered photons dominate the low energy regime of the measurement. Without proper corrections, the scattered radiation could introduce significant errors in the material decomposition, and degrade the material characterization and quantification accuracy. To mitigate the scatter problem, typically, hardware rejection and software correction algorithms can be both employed. The anti-scatter grids (ASG) are commonly used to absorb the scattered photons and help generate cleaner measurements. For semiconductor based photon counting detectors (CdTe/CdZnTe), due to charge sharing and cross-talk effects (k-escape, scatter), different ASG designs also change the detector spectral response by masking different detector areas. In this study, we will evaluate a CdZnTe based photon counting CT performance with various ASG designs at the low flux condition through simulations. The detector spectral responses with 2 different detector pixel sizes (250 um and 500um anode size) are generated by our internal simulation tool, using no ASG, 1-D and 2-D ASGs respectively. The scattered radiation is generated by GATE, a Geant4 based Monte Carlo simulation tool, using a large (33 cm diameter) cylindrical water phantom with concentric iodine/calcium inserts, and then added to the simulated phantom energy bin count measurements. The impact of the residual scatter with 1-D and 2-D ASGs in the basis and mono-energetic images will be evaluated and compared.
Accurate physics modeling of a photon counting detector is essential for detector design and performance evaluation, Computer Tomography (CT) system-level performance investigation, material decomposition, image reconstruction. The detector response is complicated because various effects involve, including fluorescence X-rays, primary electron path, charge diffusion, charge repulsion, and charge trapping. In this paper, we will present a comprehensive detector modeling approach, which incorporates all these effect into account.
Photon counting detectors are an appealing approach to spectral computed tomography for their theoretical benefits over conventional detectors. Detailed modeling and simulation is important for capturing the critical aspects of the counting and spectral performance of the detector. An approach to photon counting detector simulation is presented using a custom developed software program. The software consists of Monte-Carlo energy deposition, physics-based charge transport and current induction, and SPICE electronic simulation. It utilizes behind-the-scenes Gate for the photon interactions and energy deposition and ngspice for the SPICE electronic simulations. Various sensor geometries and definitions can be defined to simulation individual detector pixels or entire anode arrays for large-scale simulations. The simulation requires the specification of x-ray planar sources and can be specified on a per-channel basis with an energy distribution and flux. Given a sensor definition and a series of x-ray sources, the program calculates the energy-bin count read-out from each anode in the sensor array. The program can be used to study the detector response of various sensor and system geometries, including in the presence of anti-scatter grids, the performance of anti-charge sharing implementations, material decomposition algorithms, etc.
CT measurements using photon counting detectors provide spectral information that can be used to estimate a material's composition. This material decomposition task is complicated by pulse pileup and charge-sharing phenomena. Physics-based methods that use maximum likelihood to estimate a material's composition rely on accurate modeling of the forward spectral measurement process, including the source spectrum and detector response. An empirical projection-domain decomposition method is proposed that uses energy-bin measurements from known basis material path lengths. The known basis material path lengths and energy-bin measurements are used to train a neural network to model the forward spectral measurement process. The neural network is used with a maximum likelihood algorithm to estimate basis material path lengths with optimal noise properties. The method does not require a model of the source spectrum or detector response. Simulations of a step-wedge phantom containing 10 path lengths of polymethyl methacrylate and 10 path lengths of aluminum resulted in 100 calibration measurements for training. Path lengths not included in calibration were used to evaluate the estimator's performance. Projections of the test path lengths contained 1000 Poisson noise realizations and the bias and variance of the estimated path lengths were used as evaluation metrics. The proposed method had less than 2% bias in the test path lengths and had a variance that achieved the Cramèr-Rao lower bound. The proposed method is an efficient estimator that estimates basis material path lengths with optimal noise properties.
Using an energy-resolving photon counting detector, the amount of k-edge material in the x-ray path can be estimated using a process known as material decomposition. However, non-ideal effects within the detector make it difficult to accurately perform this decomposition. This work evaluated the k-edge material decomposition accuracy of two empirical estimators. A neural network estimator and a linearized maximum likelihood estimator with error look-up tables (A-table method) were evaluated through simulations and experiments. Each estimator was trained on system-specific calibration data rather than specific modeling of non-ideal detector effects or the x-ray source spectrum. Projections through a step-wedge calibration phantom consisting of different path lengths through PMMA, aluminum, and a k-edge material was used to train the estimators. The estimators were tested by decomposing data acquired through different path lengths of the basis materials. The estimators had similar performance in the chest phantom simulations with gadolinium. They estimated four of the five densities of gadolinium with less than 2mg/mL bias. The neural networks estimates demonstrated lower bias but higher variance than the A-table estimates in the iodine contrast agent simulations. The neural networks had an experimental variance lower than the CRLB indicating it is a biased estimator. In the experimental study, the k-edge material contribution was estimated with less than 14% bias for the neural network estimator and less than 41% bias for the A-table method.
Spectral CT with photon-counting detectors has the potential to improve material decomposition and contrastto-
noise ratio (CNR) compared to conventional CT. This work compared the noise properties of two general
energy-bin acquisition methods: (1) energy bins acquired from the same spectrum noise realization, and (2)
energy bins acquired from different spectrum noise realizations. For both types of acquisitions, the detected
number of counts per bin was simulated and measured on a bench-top system. The energy-bin noise standard
deviation was compared for both acquisition methods. Simulations were performed to compare both methods
with respect to noise in material decomposition estimates and the CNR in image-based weighted images. Both
the experimental and simulation results indicated increased energy-bin noise when energy measurements were
acquired from different spectrum realizations. The noise increased by a factor of 2 for the lowest energy bin,
with the noise penalty decreasing with increasing bin energy. The simulation results demonstrated a factor of 1.2
to 2 increase in noise in material decomposition estimates when acquiring from different spectrum realizations.
Despite the increased energy-bin noise, energy measurements from different spectrum realizations increased
the CNR in image-based-weighted images by 10%, potentially due to noise correlations across bins. Overall,
the investigated acquisition methods demonstrated differences in noise standard deviation, affecting material
decomposition estimates and CNR.
Photon-counting detectors with multi-bin pulse height analysis (PHA) are capable of extracting energy dependent information which can be exploited for material decomposition. Iterative decomposition algorithms have been previously implemented which require prior knowledge of the source spectrum, detector spectral response, and energy threshold settings. We experimentally investigated two material decomposition methods that do not require explicit knowledge of the source spectrum and spectral response. In the first method, the effective spectrum for each energy bin is estimated from calibration transmission measurements, followed by an iterative maximum likelihood decomposition algorithm. The second investigated method, first proposed and tested through simulations by Alvarez, uses a linearized maximum likelihood estimator which requires calibration transmission measurements. The Alvarez method has the advantage of being non-iterative. This study experimentally quantified and compared the material decomposition bias, as a percentage of material thickness, and standard deviation resulting from these two material decomposition estimators. Multi-energy x-ray transmission measurements were acquired through varying thicknesses of Teon, Delrin, and neoprene at two different flux settings and decomposed into PMMA and aluminum thicknesses using the investigated methods. In addition, a series of 200 equally spaced projections of a rod phantom were acquired over 360°. The multi-energy sinograms were decomposed using both empirical methods and then reconstructed using filtered backprojection producing two images representing each basis material. The Alvarez method decomposed Delrin into PMMA with a bias of 0.5-19% and decomposed neoprene into aluminum with a bias of less than 3%. The spectral estimation method decomposed Delrin into PMMA with a bias of 0.6-16% and decomposed neoprene into aluminum with a bias of 0.1-58%. In general, the spectral estimation method resulted in larger bias than the Alvarez method. Both methods demonstrated similar standard deviations of less than 1 mm. Both decomposition methods resulted in similar bias and standard deviation when comparing performance at the two flux levels. The results suggest preliminary feasibility of two empirical methods that use calibration measurements rather than prior knowledge of system parameters to estimate thicknesses of the basis materials.