title: A splitting-based iterative algorithm for accelerated statistical X-ray CT reconstruction.
abstract: Statistical image reconstruction using penalized weighted least-squares (PWLS) criteria can improve image-quality in X-ray computed tomography (CT). However, the huge dynamic range of the statistical weights leads to a highly shift-variant inverse problem making it difficult to precondition and accelerate existing iterative algorithms that attack the statistical model directly. We propose to alleviate the problem by using a variable-splitting scheme that separates the shift-variant and ("nearly") invariant components of the statistical data model and also decouples the regularization term. This leads to an equivalent constrained problem that we tackle using the classical method-of-multipliers framework with alternating minimization. The specific form of our splitting yields an alternating direction method of multipliers (ADMM) algorithm with an inner-step involving a "nearly" shift-invariant linear system that is suitable for FFT-based preconditioning using cone-type filters. The proposed method can efficiently handle a variety of convex regularization criteria including smooth edge-preserving regularizers and nonsmooth sparsity-promoting ones based on the l(1)-norm and total variation. Numerical experiments with synthetic and real in vivo human data illustrate that cone-filter preconditioners accelerate the proposed ADMM resulting in fast convergence of ADMM compared to conventional (nonlinear conjugate gradient, ordered subsets) and state-of-the-art (MFISTA, split-Bregman) algorithms that are applicable for CT.
authors.affiliation: Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109, USA. sramani@umich.edu
authors.forename: Sathish
authors.initials: S
authors.lastname: Ramani
authors.forename: Jeffrey A
authors.initials: JA
authors.lastname: Fessler
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D006257:Head / Q000000981:diagnostic imaging; D006801:Humans; D016018:Least-Squares Analysis; D008954:Models, Biological; D019047:Phantoms, Imaging; D011856:Radiographic Image Enhancement / Q000379:methods*; D014057:Tomography, X-Ray Computed / Q000379:methods*
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