With the increasing popularity of photon-counting detectors in X-ray computed tomography, and with virtual clinical trials playing an increasingly important role in the evaluation of imaging systems, it is vital to have accurate simulation models for photon-counting imaging systems. Physical effects such as charge sharing, Kfluorescence and Compton scattering give rise to spatiotemporal correlations between different energy bins in different pixels, and existing methods for simulating such correlations accurately with multi-pixel correlation lengths are too computationally costly to be practical for full-size CT acquisition simulations. In this work, we propose a fast, accurate method for simulating correlated Poisson noise in photon-counting detectors based on the Anscombe transformation. We use Cholesky factorization to generate correlated Gaussian random numbers and then apply the inverse Anscombe transformation to map these into approximately Poisson-distributed counts. We show that any desired correlation structure of the counts can be obtained by adjusting the mean and covariance matrix used for the Gaussian random number generation. We evaluate this method in a simulation study with both a one-dimensional "toy" model with a single energy bin and a one-dimensional "realistic" model1, by using the chi-square statistic to assess the accuracy of the marginal probability distributions and pairwise joint probability distributions. The computational speed is compared to brute-force generation of Poisson random numbers. Our results show that the proposed method achieves reasonable accuracy in approximating the Poisson distribution, with > 80% lower chi-squared than a Gaussian approximation and that it can decrease the computation time to 1% of the time required for direct Poisson generation.

Respiratory motion remains a significant challenge in computed tomography (CT), especially in thoracic imaging. Realistic motion modeling is essential to reduce artifacts and facilitate accurate diagnostics; however, acquiring the high-quality 4DCT data necessary for such modeling typically requires long scan times, which expose patients to high doses of ionizing radiation. As a result, public access to comprehensive 4DCT respiratory data is scarce. To address this problem, this report introduces a novel framework for synthesizing realistic and structurally coherent 4DCT respiratory numerical phantoms of the thoracic region from static CT images using latent diffusion models. Specifically, we propose a two-stage architecture which includes: 1. convolutional autoencoders for encoding both prior anatomical volumes and deformable vector fields (DVFs) into compact latent representations, and 2. a Res-UNet-based diffusion model used to generate latent DVFs conditioned on a full 3DCT volume prior and sampled Gaussian noise. To enforce structural coherence of the generated DVFs, a combined loss function was used incorporating bending energy and diffusion regularization. Our results show that the proposed approach can generate plausible and diverse DVFs via Denoising Diffusion Implicit Model (DDIM) sampling, enabling effective simulation of respiratory motion without requiring repeated patient scans. The results from this work can, among other things, have important implications for the training and evaluation of deep-learning-based motion compensation methods. This project's code and pretrained model weights are available at https://github.com/Axreub/ldm- respiratory- motion.

Objective.While photon-counting computed tomography (PCCT) improves image quality and reduces radiation dose, artifacts induced by cardiac and respiratory motion is still a challenge. The purpose of this work is to evaluate the potential of an image-domain motion-artifact-correction method based on a deep-learning model that incorporates spectral information (material basis images).Approach.We simulated PCCT imaging of five XCAT phantoms, and used these for training two deep neural networks-one with and one without spectral information-to map two motion-corrupted virtual monoenergetic images to corresponding motion-free images. Using images from another simulated XCAT phantom, we calculated the CT number error on five regions of interest and 10 segmented organs. The method was also evaluated visually on clinical cardiac PCCT images. Stretch quantification of endocardial engraved zones was used to calculate regional wall motion and mechanical delay. The results were compared with the motion-free image using a paired t-test.Main results.Out of 45 regions and organs, the CT number accuracy is improved in 41 regions (91%). Among these, the best accuracy is obtained with spectral information in 25 regions (61%). Both models, in particular the one with spectral information, improves visual image quality in simulated and clinical images. The model significantly (P< 0.01) improved estimation of the regional wall motion and assessment of mechanical delay of the left ventricle, but no significant difference was observed between models with and without spectral information.Significance.Our approach, validated on simulated datasets, shows that quantitative cardiac CT imaging can be improved by deep-learning motion correction and that spectral information substantially improves performance.

Purpose: When implementing differential phase-contrast imaging with current CT detectors the limited pixel size forces one to scan an analyser-grating in front of the detector to resolve the interference pattern. This simulation study compares the approach of using an analyser-grating and the approach of using a high-resolution detector to directly resolve the interference pattern by applying the non-prewhitening observer on dose-matched simulated CT scan reconstructions of the two approaches. Approach: A phantom with two concentric cylinders is used and 1000 CT scans are generated with the inner cylinder present and not present. The non-prewhitening observer is applied to the samples and the ROC curve is extracted, together with the results of a 2AFC test, the CNR, and the detectability. Results: The high-resolution approach shows a 20% increase in the phase AUC compared to the grating-based approach, with a similar increase in the 2AFC test score. The image CNR of the phase shows an increase of 134%, with the detectability increasing by 138% when compared to the grating based approach. Conclusions: An ultra-high-resolution detector, capable of directly resolving the interference pattern of differential phase-contrast imaging could change medical imaging CT as we know it. The implementation in a clinical CT would be simpler, could lower cost, and increase the dose-efficiency due to the obviation of the G(2)-grating, and at the same time provide an additional two diagnostic signals.

One advantage of photon-counting CT compared to dual-energy CT is the possibility to perform K-edge imaging, where contrast agents such as iodine can be distinguished from other substances based on spectral characteristics. However, for iodine K-edge imaging in clinical CT, the three-basis decomposition problem is ill-conditioned due to the low K-edge energy of iodine, meaning that the decomposition is highly sensitive to both noise and miscalibrations. This makes robust three-basis decomposition difficult using standard techniques. In this simulation study we evaluate a novel method of performing K-edge imaging, which circumvents the challenging three-basis decomposition step by replacing it with multiple two-basis decompositions followed by a deep convolutional neural network to generate three basis images. Based on the XCAT phantom, we generated 1224 spectral phantom image slices of the neck, with iodine-filled blood vessels and calcifications, and simulated CT imaging in CatSim with a silicon-based detector model without quantum noise, i.e. in the high-dose limit. For each simulated slice, we used maximum likelihood to perform three two-basis decompositions, into PE-PVC, PE-iodine, and PVC-iodine, yielding six basis images in total. We then trained a U-Net to map these six input images to the ground-truth basis images, PE, PVC and iodine. Our results show that the proposed method can reproduce PE, PVC and iodine basis images with high accuracy, in the high-dose limit. This suggests that the proposed three-basis decomposition method may be a feasible way of performing K-edge CT imaging with iodine, with important potential implications for imaging of the carotid arteries.

Motion artifacts are among the most important factors degrading the diagnostic performance of x-ray CT images, in particular for photon-counting CT where these artifacts can degrade the higher spatial resolution and quantitative imaging capabilities. The purpose of this simulation study is to evaluate the capability of deep neural networks to correct for motion artifacts in spectral photon-counting cardiac CT, by generating motion-corrected virtual monoenergetic images at a range of different keVs. We used CatSim to generate synthetic training data by simulating motion-corrupted and motion-free CT imaging (100 kVp, 1 s rotation) of the dynamic XCAT phantom including heart and respiratory motion. In total 2160 image pairs were generated. We trained two different neural networks for the task of estimating motion-artifact-reduced images from motion-corrupted images: one based on UNet and one based on a Wasserstein generative adversarial network with a gradient penalty (WGAN-GP). To make these networks applicable to virtual monoenergetic images at different energies, we trained them with 40 keV and 70 keV monoenergetic images as inputs and used a loss function with two terms: 1) L1-loss on soft tissue and bone basis images and 2) perceptual loss on 70 keV monoenergetic images. Our results show that the motion artifacts from 40 keV to 100 keV are reduced substantially. In conclusion, these results demonstrate the potential of image-domain deep neural networks to correct for motion artifacts in spectral cardiac CT images.

Photon-counting detectors are greatly improving the resolution and image quality in computed tomography (CT) technology. The drawback is, however, that the reconstruction becomes more challenging. This is because there is a considerable increment of the processing data due to the multiple energy bins and materials in the reconstruction analysis, as well as improved resolution. Yet efficient material decomposition and reconstruction methods tend to generate noisy images that do not completely satisfy the expected image quality. Therefore, there is a need for efficient denoising of the resulting material images. We present a new and fast denoiser that is based on a linear minimum mean square error (LMMSE) estimator. The LMMSE is very fast to compute, but not commonly used for CT image denoising, probably due to its inability to adapt the amount of denoising to different parts of the image and the difficulty to derive accurate statistical properties from the CT data. To overcome these problems we propose a model-based deep learning strategy, that is, a deep neural network that preserves an LMMSE structure (model-based), providing more robustness unseen data, as well as good interpretability to the result. In this way, the solution adapts to the anatomy in every point of the image and noise properties at that particular location. In order to asses the performance of the new method, we compare it to both to a conventional LMMSE estimator and to a “black-box” CNN in a simulation study with anthropomorphic phantoms.

Deep learning (DL) has proven to be an important tool for high quality image denoising in low-dose and photon-counting CT. However, DL models are usually trained using supervised methods, requiring paired data that may be difficult to obtain in practice. Physics-inspired generative models, such as score-based diffusion models, offer unsupervised means of solving a wide range of inverse problems via posterior sampling. The latest in this family are Poisson flow generative models (PFGM)++ which, inspired by electrostatics, treat the $N$-dimensional data as positive electric charges in a $N+D$-dimensional augmented space. The electric field lines generated by these charges are used to find an invertible mapping, via an ordinary differential equation, between an easy-to-sample prior and the data distribution of interest. In this work, we propose a method for CT image denoising based on PFGM++ that does not require paired training data. To achieve this, we adapt PFGM++ for solving inverse problems via posterior sampling, by hijacking and regularizing the sampling process. Our method incorporates score-based diffusion models (EDM) as a special case as $D\rightarrow \infty$, but additionally allows trading off robustness for rigidity by varying $D$. The network is efficiently trained on randomly extracted patches from clinical normal-dose CT images. The proposed method demonstrates promising performance on clinical low-dose CT images and clinical images from a prototype photon-counting system.

Cadmium telluride (CdTe) is one of the materials used in photon-counting detectors for x-ray computed tomography. One challenge with this material is that it is susceptible to polarisation due to holes being trapped in impurities in the material. This can potentially lead to the buildup of bulk charge in the semiconductor, causing decreased charge collection efficiency and degraded energy resolution. In this work, we develop a simulation model of CdTe detectors with polarisation and use it to study the effect of polarisation on the measured energy spectrum for different charge collection times. To this end, we use a theoretical model of charge buildup to find the critical charge in the detector’s bulk above which the detector can be considered completely polarised. We then simulate a 320-by-270-by-1600 μm CdTe detector used in CT clinical imaging, for varying degrees of polarisation (ratio between the actual charge and the critical charge) and charge collection time. Our results show that the measured spectrum gets heavily distorted for large degrees of polarisation or for short charge collection time. We also put these results in context by discussing how they relate to the critical fluence rate and the time of flight of the charge carriers. These results can lead to improved simulation models of CdTe detectors and a better understanding the factors affecting their imaging performance.

Photon-counting detectors (PCD) are the most recent advancement in computed tomography (CT). PCDs allow, among other things, for material decomposition, which decomposes the imaged object into a set of basis materials. Another field that is gaining attention, is the use of deep learning to improve the image reconstruction process in CT. In this work, we study the use of deep learning, specifically convolutional neural networks trained on the KiTS19 Challenge kidney data set, to improve the image quality of basis images resulting from three-material decomposition, a problem that is difficult due to its high sensitivity to noise. Our objective is to compare different network architectures and investigate whether these are best implemented in the projection domain or in the image domain. We study three different network architectures: U-Net, Dilated U-Net and ResNet, each applied in either the image domain or in the projection domain. The resulting image quality is evaluated in terms of contrast-to-noise ratio, task transfer function and noise power spectrum. Results show that for the type of phantoms the networks were trained on, the most effective option is to implement the network in the image domain and to use either the U-Net or Dilated U-Net architectures. However, when applying the networks to other phantoms, it seems that the networks in the sinogram generalize better, and produce better results. We also discuss why this might be the case, compare it with previous research, and consider what further improvements can be made.

Photon-counting CT (PCCT) offers improved diagnostic performance through better spatial and energy resolution, but developing high-quality image reconstruction methods that can deal with these large datasets is challenging. Model-based solutions incorporate models of the physical acquisition in order to reconstruct more accurate images, but are dependent on an accurate forward operator and present difficulties with finding good regularization. Another approach is deep-learning reconstruction, which has shown great promise in CT. However, fully data-driven solutions typically need large amounts of training data and lack interpretability. To combine the benefits of both methods, while minimizing their respective drawbacks, it is desirable to develop reconstruction algorithms that combine both model-based and data-driven approaches. In this work, we present a novel deep-learning solution for material decomposition in PCCT, based on an unrolled/unfolded iterative network. We evaluate two cases: a learned post-processing, which implicitly utilizes model knowledge, and a learned gradient-descent, which has explicit model-based components in the architecture. With our proposed techniques, we solve a challenging PCCT simulation case: three-material decomposition in abdomen imaging with low dose, iodine contrast, and a very small training sample support. In this scenario, our approach outperforms a maximum likelihood estimation, a variational method, as well as a fully-learned network.

Photon-counting CT scanners promise improvements in terms of noise performance, spatial resolution and material-discrimination capabilities, and their ability to reject electronic noise gives them a particularly large advantage for low-dose imaging compared to energy-integrating CT. Since filtered backprojection is suboptimal for highly noisy image data, model-based iterative reconstruction can be expected to give improved image quality for low-dose CT imaging. Several ”one-step” algorithms have been proposed that combine material decomposition and image reconstruction in a single optimization problem. The purpose of this simulation study is to evaluate the image quality that can be achieved with a one-step model-based iterative reconstruction for photon-counting low-dose CT. To this end, a penalized Poisson-likelihood model is used to reconstruct material basis images and virtual monoenergetic images from simulated measurements with a silicon-based photon-counting CT scanner and study the resulting image quality in terms of the edge-spread function, contrast-to-noise ratio and noise power spectrum, so that the tradeoff between noise and spatial resolution can be studied. The results are compared with a two-step method where projection-space material decomposition is followed by filtered backprojection. Our results show that the unconstrained one-step method can give good image quality even for low-dose images where the unconstrained two-step method fails. These results demonstrate the potential of photon-counting CT for low-dose imaging applications.

The introduction of photon-counting detectors in x-ray computed tomography raises the question of how reconstruction algorithms should be adapted to photon-counting measurement data. The transition from energy-integrating to photon-counting detectors introduces new effects into the data model, such as pure Poisson statistics and increased cross talk between detector pixels, (e.g. due to charge sharing), but it is still not known in detail how these effects can be treated accurately by the reconstruction algorithm. In this work, we propose a new reconstruction method based on penalized-likelihood reconstruction that incorporates these effects. By starting from a simple, easily-solved reconstruction problem and adding correction terms for the additional physical effects, we obtain a series expansion for the solution to the image reconstruction problem. This approach serves the twofold purpose of (1) yielding a new, potentially faster method of incorporating complex detector models in the reconstruction process and (2) providing insight into the impact of the non-ideal physical effects on the reconstructed image. We investigate the potential for reconstructing images from simulated photon-counting energy-resolving CT data with the new algorithm by including correction terms representing pure Poisson statistics and interpixel cross talk; and we investigate the impact of these physical effects on the reconstructed images. Results indicate that using two correction terms gives good agreement with the converged solution, suggesting that the new method is feasible in practice. This new approach to image reconstruction can help in developing improved reconstruction algorithms for photon-counting CT.