A Splitting-Based Iterative Algorithm for Accelerated Statistical X-Ray CT Reconstruction

S. Ramani

doi:10.1109/TMI.2011.2175233

2012-03-01

224

S. Ramani *

Jeffrey A. Fessler

DOI：10.1109/TMI.2011.2175233

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摘要

En 中文

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 non-smooth 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.

Keyword:

Alternating minimization

iterative algorithm

method of multipliers

regularization

statistical image reconstruction