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

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 acce...

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Bibliographic Details
Published in:IEEE transactions on medical imaging Vol. 31; no. 3; pp. 677 - 688
Main Authors: Ramani, S., Fessler, J. A.
Format: Journal Article
Language:English
Published: United States IEEE 01.03.2012
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Acceleration
Algorithms
Alternating minimization
Computed tomography
Computer Simulation
Convergence
Head - diagnostic imaging
Humans
Image reconstruction
iterative algorithm
Iterative methods
Least-Squares Analysis
method of multipliers
Minimization
Models, Biological
Optimization
Phantoms, Imaging
Radiographic Image Enhancement - methods
regularization
statistical image reconstruction
Studies
Tomography, X-Ray Computed - methods
ISSN:0278-0062, 1558-254X, 1558-254X
Online Access:Get full text
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Summary: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.
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ISSN:0278-0062
1558-254X
1558-254X
DOI:10.1109/TMI.2011.2175233