Accelerated statistical image reconstruction algorithms and simplified cost functions for X-ray computed tomography

Statistical image reconstruction methods are poised to replace traditional methods like filtered back-projection (FBP) in commercial X-ray computed tomography (CT) scanners. Statistical methods offer many advantages over FBP, including incorporating physical effects and physical constraints, modeling of complex imaging geometries, and imaging at lower X-ray doses. But, the use of statistical methods is limited due to many practical problems. This thesis proposes methods to improve four aspects of statistical methods: reconstruction time, beam hardening, non-negativity constraints, and organ motion. To reduce the reconstruction time, several novel iterative algorithms are proposed that are adapted to multi-core computing, including a hybrid ordered subsets (OS)/iterative coordinate descent (ICD) approach. This approach leads to a reduction in reconstruction time, and it also makes the ICD algorithm robust to the initial guess image. Statistical methods have accounted for beam hardening by using more information than needed by traditional FBP-based methods like the Joseph-Spital (JS) method. This thesis proposes a statistical method that uses exactly the same beam hardening information as the JS method while suppressing beam hardening artifacts. Directly imposing the non-negativity constraints can increase the computation time of algorithms such as the preconditioned conjugate gradient (PCG) method. This thesis proposes a modification of the penalized-likelihood cost function for monoenergetic transmission tomography, and a corresponding PCG algorithm, that reduce reconstruction time when enforcing nonnegativity. Organ motion during a scan causes image artifacts, and in some cases these artifacts are more apparent when standard statistical methods are used. A preliminary simulation study of a new approach to remove motion artifacts is presented. The distinguishing feature of this approach is that it does not require any new information from the scanner. The target applications of this research effort are 3-D volume reconstructions for axial cone-beam and helical cone-beam scanning geometries of multislice CT (MSCT) scanners.