<b>Advanced Algorithms for X-ray CT Image Reconstruction and Processing</b>

X-ray computed tomography (CT) is one of the most widely used imaging modalities for medical diagnosis. Improving the quality of clinical CT images while keeping the X-ray dosage of patients low has been an active area of research. Recently, there have been two major technological advances in the commercial CT systems. The first is the use of Deep Neural Networks (DNN) to denoise and sharpen CT images, and the second is use of photon counting detectors (PCD) which provide higher spectral and spatial resolution compared to the conventional energy-integrating detectors. While both techniques have potential to improve the quality of CT images significantly, there are still challenges to improve the quality further.A denoising or sharpening algorithm for CT images must retain a favorable texture which is critically important for radiologists. However, commonly used methodologies in DNN training produce over-smooth images lacking texture. The lack of texture is a systematic error leading to a biased estimator.In the first portion of this thesis, we propose three algorithms to reduce the bias, thereby to retain the favorable texture. The first method proposes a novel approach to designing a loss function that penalizes bias in the image more while training a DNN, producing more texture and detail in results. Our experiments verify that the proposed loss function outperforms the commonly used mean squared error loss function. The second algorithm proposes a novel approach to designing training pairs for a DNN-based sharpener. While conventional sharpeners employ noise-free ground truth producing over-smooth images, the proposed Noise Preserving Sharpening Filter (NPSF) adds appropriately scaled noise to both the input and the ground truth to keep the noise texture in the sharpened result similar to that of the input. Our evaluations show that the NPSF can sharpen noisy images while producing desired noise level and texture. The above two algorithms merely control the amount of texture retained and are not designed to produce texture that matches to a target texture. A Generative Adversarial Network (GAN) can produce the target texture. However, naive application of GANs can introduce inaccurate or even unreal image detail. Therefore, we propose a Texture Matching GAN (TMGAN) that uses parallel generators to separate anatomical features from the generated texture, which allows the GAN to be trained to match the target texture without directly affecting the underlying CT image. We demonstrate that TMGAN generates enhanced image quality while also producing texture that is desirable for clinical application.In the second portion of this research, we propose a novel algorithm for the optimal statistical processing of photon-counting detector data for CT reconstruction. Current reconstruction and material decomposition algorithms for photon counting CT are not able to utilize simultaneously both the measured spectral information and advanced prior models. We propose a modular framework based on Multi-Agent Consensus Equilibrium (MACE) to obtain material decomposition and reconstructions using the PCD data. Our method employs a detector agent that uses PCD measurements to update an estimate along with a prior agent that enforces both physical and empirical knowledge about the material-decomposed sinograms. Importantly, the modular framework allows the two agents to be designed and optimized independently. Our evaluations on simulated data show promising results.