Quadratic regularization design for fan beam transmission tomography

Abstract

Statistical methods for tomographic image reconstruction have shown considerable potential for improving image quality in X-ray CT. Penalized-likelihood (PL) image reconstruction methods require maximizing an objective function that is based on the log-likelihood of the sinogram measurements and on a roughness penalty function to control noise. In transmission tomography, PL methods (and MAP methods) based on conventional quadratic regularization functions lead to nonuniform and anisotropic spatial resolution, even for idealized shift-invariant imaging systems. We have previously addressed this problem for parallel-beam emission tomography by designing data-dependent, shift-variant regularizers that improve resolution uniformity. This paper extends those methods to the fan-beam geometry used in X-ray CT imaging. Simulation results demonstrate that the new method for regularization design requires very modest computation and leads to nearly uniform and isotropic spatial resolution in the fan-beam geometry when using quadratic regularization.