Iterative reconstruction methods of CT images using a statistical framework

Medical imaging technologies play a vital role in early diagnosis of disease by providing internal images of the human body to medical professionals. Computed Tomography (CT) is currently the most commonly used medical imaging technology because it is easy to use, detectors and scanners are constantly improving, and more importantly, patients receive less radiation compared to other imaging technologies. This thesis focuses on improving CT reconstruction algorithms by incorporating prior knowledge of the tissues being scanned. A Gaussian Mixture Prior, and Gibbs sampling is introduced into the reconstruction framework and solved using Maximum-a-posterior (MAP). As a comparison, the images were also reconstructed using unregularized and regularized Maximum Likelihood (ML)

Discrete Tomography by Convex-Concave Regularization using Linear and Quadratic Optimization

Discrete tomography concerns the reconstruction of objects that are made up from a few different materials, each of which comprising a homogeneous density distribution. Under the assumption that these densities are a priori known new algorithms can be developed which typically need less projection data to reveal appealing reconstruction results