Multimedia Tools and Applications

, Volume 77, Issue 10, pp 12853–12869 | Cite as

Image compressed sensing based on non-convex low-rank approximation

  • Yan Zhang
  • Jichang GuoEmail author
  • Chongyi Li


Nonlocal sparsity and structured sparsity have been evidenced to improve the reconstruction of image details in various compressed sensing (CS) studies. The nonlocal processing is achieved by grouping similar patches of the image into the groups. To exploit these nonlocal self-similarities in natural images, a non-convex low-rank approximation is proposed to regularize the CS recovery in this paper. The nuclear norm minimization, as a convex relaxation of rank function minimization, ignores the prior knowledge of the matrix singular values. This greatly restricts its capability and flexibility in dealing with many practical problems. In order to make a better approximation of the rank function, the non-convex low-rank regularization namely weighted Schatten p-norm minimization (WSNM) is proposed. In this way, both the local sparsity and nonlocal sparsity are integrated into a recovery framework. The experimental results show that our method outperforms the state-of-the-art CS recovery algorithms not only in PSNR index, but also in local structure preservation.


Image compressed sensing Low-rank approximation Weighted Schatten p-norm Non-convex optimization 



The authors would like to give thanks to the anonymous reviewers for their valuable comments that were useful to improve the quality of the paper. This work was supported by Natural Science Foundation of Tianjin (Grant No. 15JCYBJC15500).


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© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.School of Electronic Information EngineeringTianjin UniversityTianjinChina
  2. 2.School of Computer and Information EngineeringTianjin Chengjian UniversityTianjinChina

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