There is provided a method and corresponding system for image reconstruction based on energy-resolved x-ray data. The method comprises collecting (S1) at least one representation of energy-resolved x-ray data, and performing (S2) at least two basis material decompositions based on said at least one representation of energy-resolved x-ray data to generate at least two original basis image representation sets. The method further comprises obtaining or selecting (S3) at least two basis image representations from at least two of said original basis image representation sets, and processing (S4) said obtained or selected basis image representations by data processing based on machine learning to generate at least one representation of output image data.

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.

Disclosed is a calibration phantom for an x-ray imaging system having an x-ray source and an x-ray detector. The calibration phantom includes a combination of geometric objects of at least three different types and/or compositions including: a first object located in the middle, including a first material; a plurality of second objects arranged around the periphery of the first object, at least a subset of the second objects including a second material different than the first material, wherein the first object is relatively larger than the second objects; a plurality of third objects arranged around the periphery of the first object and/or around the periphery of at least a subset of the second objects, at least a subset of the third objects including a third material different than the first material and the second material, wherein the third objects are relatively smaller than the second objects.

X-ray computed tomography (CT) is a widely used imaging modality that enables visualization of nearly every part of the human body. It is used for diagnosis of disease and injury as well as medical treatment planning. The vast majority of CT scanners in clinical use today have energy-integrating x-ray detectors, which measure the total incident energy in a given measurement.Spectral photon-counting detectors operate by counting individual photons and measuring their energy, and are expected to yield the next major advance in CT, with improvements in spatial resolution, dose efficiency, material differentiation and quantitative imaging capabilities compared to the current state-of-the-art.

In this Thesis, a set of new models and applications for a spectral photon-counting silicon detector developed for CT is investigated. The first part of the Thesis is dedicated to the modeling of spectral photon-counting silicon detectors. A new statistical model for the effects of pulse pileup is presented. Also, the effects on image quality from intra-detector Compton scatter in silicon detectors are investigated via spatio-energetic modeling. In the second part of the Thesis, potential applications for spectral photon-counting detectors are investigated. An experimental study of ex vivo CT imaging of an excised human heart with calcified plaque is presented. It demonstrates the feasibility of unconstrained projection-based three-material decomposition with iodine as a third basis material and explores the potential improvements in spatial resolution and material differentiation that can be achieved with a spectral photon-counting silicon detector compared to a conventional dual-energy CTsystem. Two other applications are investigated with simulations: a method for reconstructing CT images from spectral photon-counting CT data that accurately mimic conventional CT images; and a method for estimating iron concentration in mixtures of liver and adipose tissue when using three basis functions instead of only two to describe the linear attenuation coefficient of tissues in the human body. 

Although the methods presented in this Thesis have been specifically developed for a spectral photon-counting silicon detector, they are also applicable for other types of photon-counting detectors.

Photon counting detectors in x-ray computed tomography (CT) improve the decomposition of the CT scans into different materials. This decomposition is however not straightforward to solve, both in terms of computation expense and Photon counting detectors in x-ray computed tomography (CT) are a major technological advancement that provides additional energy information, and improve the decomposition of the CT image into material images. This material decomposition problem is however a non-linear inverse problem that is difficult to solve, both in terms of computation expense and accuracy. The most accepted solution consists in defining an optimization problem based on a maximum likelihood (ML) estimate with Poisson statistics, which is a model-based approach very dependent on the considered forward model and the chosen optimization solver. This may make the material decomposition result noisy and slow to be computed. To incorporate data-driven enhancement to the ML estimate, we propose a deep learning post-processing technique. Our approach is based on convolutional residual blocks that mimic the updates of an iterative optimization process and consider the ML estimate as an input. Therefore, our architecture implicitly considers the physical models of the problem, and in consequence needs less training data and fewer parameters than other standard convolutional networks typically used in medical imaging. We have studied a simulation case of our deep learning post-processing, first on a set of 350 Shepp-Logan -based phantoms, and then in a 600 human numerical phantoms. Our approach has shown denoising enhancement over two different ray-wise decomposition methods: one based on a Newton’s method to solve the ML estimation, and one based on a linear least-squares approximation of the ML expression. We believe this new deep learning post-processing approach is a promising technique to denoise material-decomposed sinograms in photon-counting CT.

An x-ray imaging apparatus includes an x-ray source and detector with multiple detector elements. The source and detector are on a support that rotates around a subject, enabling projections at different view angles. The apparatus operates the x-ray source in switched kVp mode for alternately applying different voltages, including lower and higher voltages, during rotation to enable lower-energy and higher-energy exposures over the projections, providing for lower-energy projections and higher-energy projections. The x-ray detector is a photon-counting multi-bin detector allocating photon counts to multiple energy bins, and the apparatus selects counts from at least a subset of the bins to provide corresponding photon count information for both lower- and higher-energy projections. The apparatus performs material basis decomposition for some of the lower-energy projections and higher-energy projections and/or for some combinations of at least one lower-energy projection and at least one higher-energy projection, based on the corresponding photon count information.

An important question when developing photon-counting detectors for computed tomography is how to select energy thresholds. In this work thresholds are optimized by maximizing signal-difference-to-noise ratio squared (SDNR2) in an optimally weighted image and signal-to-noise ratio squared (SNR2) in a gadolinium basis image in a silicon-strip detector and a cadmium zinc telluride (CZT) detector, factoring in pileup and imperfect energy response based on real-world detector systems. To investigate to what extent one single set of thresholds could be applied in various imaging tasks, the robustness of optimal thresholds with 2 to 8 bins is examined with the variation of phantom thicknesses, target materials and detector configurations. In contrast to previous studies, the optimal threshold locations do not always increase with increasing attenuation if pileup is included. With respect to the tradeoff between higher SDNR2 or SNR2 and less data, setting optimal thresholds for a 30 cm phantom yields robust SDNR2 and setting optimal thresholds for a 50 cm phantom yields robust SNR2 with 6 to 8 bins in the silicon-strip detector. Furthermore, setting optimal thresholds for a 30 cm phantom yields robust SDNR2 or SNR2 with 6 to 8 bins and a pixel size less than or equal to 0.5 x 0.5 mm(2) in the CZT detector.