Iterative Algorithms for Volumetric X-ray Computed Tomography

Abstract

Cone beam computed tomography (CBCT) enables a volumetric image reconstructionfrom a set of 2D projection data. This thesis studies the performanceof a wide range iterative algorithms in various aspects, aiming togenerate a better CBCT image reconstruction, especially when projectiondata is limited. We have implemented a wide range of algebraic iterativealgorithms. Hence, the performance of ART, SART and OS-SART is studiedbased on a range of image quality measures. The major limitations oftraditional iterative methods are their computational time. The conjugategradients (CG) algorithm and its variants can be used to solve linear systemsof equations arising from CBCT. Their applications can be found ina general linear algebra context, but in tomography problems (e.g. CBCTreconstruction) they have not widely been used. Hence, CBCT reconstructionusing the CG-type algorithm LSQR was implemented and studied. InCBCT reconstruction, the main computational challenge is that the matrixA usually is very large, and storing it in full requires an amount of memorywell beyond the reach of commodity computers. Because of these memorycapacity constraints, only a small fraction of the weighting matrix Ais typically used, leading to a poor reconstruction. In this final part of thethesis, to overcome this diculty, the matrix A is partitioned and storedblockwise, and blockwise matrix-vector multiplications are implementedwithin LSQR. This implementation allows us to use the full weightingmatrix A for CBCT reconstruction without further enhancing computerstandards. Tikhonov regularization has been developed in this framework,and can produce significant improvement in the reconstructed images forlimited data case.

Date of Award	11 Dec 2012
Original language	English
Awarding Institution	University of Bath
Supervisor	Manuchehr Soleimani (Supervisor)