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Mathematical Problems in Engineering
Volume 2018 (2018), Article ID 7171352, 15 pages
Research Article

Content-Aware Compressive Sensing Recovery Using Laplacian Scale Mixture Priors and Side Information

1School of Electronic and Information Engineering, South China University of Technology, Guangzhou 510641, China
2School of Electronic and Information Engineering, Nanjing University of Information Science & Technology, Nanjing 210044, China

Correspondence should be addressed to Lihong Ma; nc.ude.tucs@amhlee

Received 10 August 2017; Revised 3 November 2017; Accepted 20 November 2017; Published 29 January 2018

Academic Editor: Raffaele Solimene

Copyright © 2018 Zhonghua Xie 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.


Nonlocal methods have shown great potential in many image restoration tasks including compressive sensing (CS) reconstruction through use of image self-similarity prior. However, they are still limited in recovering fine-scale details and sharp features, when rich repetitive patterns cannot be guaranteed; moreover the CS measurements are corrupted. In this paper, we propose a novel CS recovery algorithm that combines nonlocal sparsity with local and global prior, which soften and complement the self-similarity assumption for irregular structures. First, a Laplacian scale mixture (LSM) prior is utilized to model dependencies among similar patches. For achieving group sparsity, each singular value of similar packed patches is modeled as a Laplacian distribution with a variable scale parameter. Second, a global prior and a compensation-based sparsity prior of local patch are designed in order to maintain differences between packed patches. The former refers to a prediction which integrates the information at the independent processing stage and is used as side information, while the latter enforces a small (i.e., sparse) prediction error and is also modeled with the LSM model so as to obtain local sparsity. Afterward, we derive an efficient algorithm based on the expectation-maximization (EM) and approximate message passing (AMP) frame for the maximum a posteriori (MAP) estimation of the sparse coefficients. Numerical experiments show that the proposed method outperforms many CS recovery algorithms.