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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 137616, 13 pages
Research Article

Approximate Sparsity and Nonlocal Total Variation Based Compressive MR Image Reconstruction

Department of Information Engineering, Nanchang Institute of Technology, Nanchang, China

Received 27 March 2014; Revised 11 August 2014; Accepted 14 August 2014; Published 28 August 2014

Academic Editor: Fatih Yaman

Copyright © 2014 Chengzhi Deng 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.


Recent developments in compressive sensing (CS) show that it is possible to accurately reconstruct the magnetic resonance (MR) image from undersampled -space data by solving nonsmooth convex optimization problems, which therefore significantly reduce the scanning time. In this paper, we propose a new MR image reconstruction method based on a compound regularization model associated with the nonlocal total variation (NLTV) and the wavelet approximate sparsity. Nonlocal total variation can restore periodic textures and local geometric information better than total variation. The wavelet approximate sparsity achieves more accurate sparse reconstruction than fixed wavelet and norm. Furthermore, a variable splitting and augmented Lagrangian algorithm is presented to solve the proposed minimization problem. Experimental results on MR image reconstruction demonstrate that the proposed method outperforms many existing MR image reconstruction methods both in quantitative and in visual quality assessment.