title: Quadratic regularization design for 2-D CT.
abstract: Statistical methods for tomographic image reconstruction have improved noise and spatial resolution properties that may improve image quality in X-ray computed tomography (CT). Penalized weighted least squares (PWLS) methods using conventional quadratic regularization lead to nonuniform and anisotropic spatial resolution due to interactions between the weighting, which is necessary for good noise properties, and the regularizer. Previously, we addressed this problem for parallel-beam emission tomography using matrix algebra methods to design data-dependent, shift-variant regularizers that improve resolution uniformity. This paper develops a fast angular integral mostly analytical (AIMA) regularization design method for 2-D fan-beam X-ray CT imaging, for which parallel-beam tomography is a special case. Simulation results demonstrate that the new method for regularization design requires very modest computation and leads to nearly uniform and isotropic spatial resolution in transmission tomography when using quadratic regularization.
authors.affiliation: Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109 USA. hugoshi@umich.edu
authors.forename: Hugo R
authors.initials: HR
authors.lastname: Shi
authors.forename: Jeffrey A
authors.initials: JA
authors.lastname: Fessler
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D005583:Fourier Analysis; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D016018:Least-Squares Analysis; D019047:Phantoms, Imaging; D014057:Tomography, X-Ray Computed