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Computational and Mathematical Methods in Medicine
Volume 2016 (2016), Article ID 1724630, 14 pages
http://dx.doi.org/10.1155/2016/1724630
Research Article

Sparse Parallel MRI Based on Accelerated Operator Splitting Schemes

1School of Information Engineering, Guangdong University of Technology, Guangzhou 510006, China
2Paul C. Lauterbur Research Centre for Biomedical Imaging, Shenzhen Institutes of Advanced Technology, Shenzhen, China
3Shenzhen Key Laboratory for MRI, Shenzhen, Guangdong, China

Received 26 April 2016; Accepted 29 August 2016

Academic Editor: Po-Hsiang Tsui

Copyright © 2016 Nian Cai et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Recently, the sparsity which is implicit in MR images has been successfully exploited for fast MR imaging with incomplete acquisitions. In this paper, two novel algorithms are proposed to solve the sparse parallel MR imaging problem, which consists of regularization and fidelity terms. The two algorithms combine forward-backward operator splitting and Barzilai-Borwein schemes. Theoretically, the presented algorithms overcome the nondifferentiable property in regularization term. Meanwhile, they are able to treat a general matrix operator that may not be diagonalized by fast Fourier transform and to ensure that a well-conditioned optimization system of equations is simply solved. In addition, we build connections between the proposed algorithms and the state-of-the-art existing methods and prove their convergence with a constant stepsize in Appendix. Numerical results and comparisons with the advanced methods demonstrate the efficiency of proposed algorithms.