Reconstruction Algorithms for Spectral Computed Tomography

Abstract

In this thesis, reconstruction algorithms for spectral computed tomography are studied and tested. A reconstruction algorithm for inverse problem usually consists of: (1) formulating an optimization problem that includes a data fidelity term and a regularization term; (2) applying a proper numerical method to solve the optimization problem. The first part of the thesis works on single-energy reconstructions, with a focus on effects of regularization terms and acceleration techniques. When turning to the spectral CT, a general reconstruction framework is formulated, and a two-step algorithm is then developed and tested. Numerical experiments have shown that the two-step algorithm can reconstruct the material-specific images from spectral data, and that the two-step reconstruction can be computed efficiently after applying proper numerical methods.