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SIAM J. on Imaging Sciences / Volume 5 / Issue 1

SIAM J. Imaging Sci. 5, pp. 90-118 (29 pages)

Fast Algorithms for Image Reconstruction with Application to Partially Parallel MR Imaging

Yunmei Chen, William Hager, Feng Huang, Dzung Phan, Xiaojing Ye, and Wotao Yin

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This paper presents two fast algorithms for total variation–based image reconstruction in a magnetic resonance imaging technique known as partially parallel imaging (PPI), where the inversion matrix is large and ill-conditioned. These algorithms utilize variable splitting techniques to decouple the original problem into more easily solved subproblems. The first method reduces the image reconstruction problem to an unconstrained minimization problem, which is solved by an alternating proximal minimization algorithm. One phase of the algorithm solves a total variation (TV) denoising problem, and the second phase solves an ill-conditioned linear system. Linear and sublinear convergence results are given, and an implementation based on a primal-dual hybrid gradient (PDHG) scheme for the TV problem and on a Barzilai–Borwein scheme for the linear inversion is proposed. The second algorithm exploits the special structure of the PPI reconstruction problem by decomposing it into one subproblem involving Fourier transforms and another subproblem that can be treated by the PDHG scheme. Numerical results and comparisons with recently developed methods indicate the efficiency of the proposed algorithms.

© 2012 Society for Industrial and Applied Mathematics

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KEYWORDS

AMS Subject Headings

90C25, 68U10, 65J22

PUBLICATION DATA

ISSN

1936-4954 (online)

Publisher

$abstract.society.value is a Member of CrossRef Society for Industrial and Applied Mathematics

ARTICLE DATA

History
Received April 19, 2010
Accepted October 24, 2011
Published online January 24, 2012
Digital Object Identifier
http://dx.doi.org/10.1137/100792688

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