Journal
INFORMATION SCIENCES
Volume 451, Issue -, Pages 161-179Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.ins.2018.03.064
Keywords
CS-MRI; Group sparsity; Dictionary learning; Nonconvex optimization; Low rank
Categories
Funding
- National Natural Science Foundation of China [61701055, 61501072, 61571069, 61675036, 61471073]
- Basic and Advanced Research Project in Chongqing [cstc2016jcyjA0134]
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Compressed sensing MRI (CS-MRI) significantly accelerates scanning time via accurate reconstruction of the image from undersampled k-space data. In this work, combining two priors of sparsity and nonlocal similarity, an algorithm of group sparsity with an orthogonal dictionary (GSOD) is proposed to realize CS-MRI reconstruction within an optimization framework. To efficiently solve the resultant non-convex optimization, a lower bound of the original problem is derived, and generalized soft-thresholding is then applied to obtain the solution from that lower bound in a fast and accurate manner. Moreover, considering the important role of the dictionary in sparse representation, a modified GSOD (M-GSOD) approach is also developed in which the orthogonal dictionary is adaptively learned from the group. It is proven that the proposed sparse coding model in the M-GSOD is equivalent to the low-rank model, and the connection between the two independent models is established for the first time. Finally, a fast and accurate algorithm to solve M-GSOD is provided. Compared with the current methods, the proposed methods demonstrate a state-of-the-art performance, which shows the correctness of the non-convex regularization and optimal dictionary learning. (C) 2018 Elsevier Inc. All rights reserved.
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