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BioMed Research International
Volume 2016 (2016), Article ID 2860643, 7 pages
Research Article

Two-Layer Tight Frame Sparsifying Model for Compressed Sensing Magnetic Resonance Imaging

1Paul C. Lauterbur Research Center for Biomedical Imaging, Shenzhen Institutes of Advanced Technology, Shenzhen, Guangdong 518055, China
2The Beijing Center for Mathematics and Information Interdisciplinary Sciences, Beijing 100048, China
3Biomedical and Multimedia Information Technology (BMIT) Research Group, School of Information Technologies, The University of Sydney, Sydney, NSW 2006, Australia
4Nanchang University, Nanchang, Jiangxi, China

Received 20 April 2016; Revised 5 August 2016; Accepted 18 August 2016

Academic Editor: Andrey Krylov

Copyright © 2016 Shanshan Wang 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.


Compressed sensing magnetic resonance imaging (CSMRI) employs image sparsity to reconstruct MR images from incoherently undersampled -space data. Existing CSMRI approaches have exploited analysis transform, synthesis dictionary, and their variants to trigger image sparsity. Nevertheless, the accuracy, efficiency, or acceleration rate of existing CSMRI methods can still be improved due to either lack of adaptability, high complexity of the training, or insufficient sparsity promotion. To properly balance the three factors, this paper proposes a two-layer tight frame sparsifying (TRIMS) model for CSMRI by sparsifying the image with a product of a fixed tight frame and an adaptively learned tight frame. The two-layer sparsifying and adaptive learning nature of TRIMS has enabled accurate MR reconstruction from highly undersampled data with efficiency. To solve the reconstruction problem, a three-level Bregman numerical algorithm is developed. The proposed approach has been compared to three state-of-the-art methods over scanned physical phantom and in vivo MR datasets and encouraging performances have been achieved.