University of Oulu

Zhiyuan Z., Xinggan Z., Qiong W., Lan T., Xin L. Group-based sparse representation for image compressive sensing reconstruction with non-convex regularization. Neurocomputing, Volume 296, 2018, Pages 55-63, ISSN 0925-2312.

Group-based sparse representation for image compressive sensing reconstruction with non-convex regularization

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Author: Zha, Zhiyuan1; Zhang, Xinggan1; Wang, Qiong1;
Organizations: 1School of Electronic Science and Engineering, Nanjing University, Nanjing 210023, China
2National Mobile Commun. Research Lab., Southeast University, Nanjing 210023, China
3The Center for Machine Vision and Signal Analysis, University of Oulu, 90014, Finland
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 1.7 MB)
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Language: English
Published: Elsevier, 2018
Publish Date: 2020-03-21


Patch-based sparse representation modeling has shown great potential in image compressive sensing (CS) reconstruction. However, this model usually suffers from some limits, such as dictionary learning with great computational complexity, neglecting the relationship among similar patches. In this paper, a group-based sparse representation method with non-convex regularization (GSR-NCR) for image CS reconstruction is proposed. In GSR-NCR, the local sparsity and nonlocal self-similarity of images is simultaneously considered in a unified framework. Different from the previous methods based on sparsity-promoting convex regularization, we extend the non-convex weighted ℓp (0 < p < 1) penalty function on group sparse coefficients of the data matrix, rather than conventional ℓ1-based regularization. To reduce the computational complexity, instead of learning the dictionary with a high computational complexity from natural images, we learn the principle component analysis (PCA) based dictionary for each group. Moreover, to make the proposed scheme tractable and robust, we have developed an efficient iterative shrinkage/thresholding algorithm to solve the non-convex optimization problem. Experimental results demonstrate that the proposed method outperforms many state-of-the-art techniques for image CS reconstruction.

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Series: Neurocomputing
ISSN: 0925-2312
ISSN-E: 1872-8286
ISSN-L: 0925-2312
Volume: 296
Pages: 55 - 63
DOI: 10.1016/j.neucom.2018.03.027
Type of Publication: A1 Journal article – refereed
Field of Science: 113 Computer and information sciences
Funding: The first author Zhiyuan Zha thanks to God for meeting Dr. Jie Zhang of Beihang University. Jie Zhang is the best beautiful girl in Zhiyuan’s heart and Zhiyuan wants to love Jie all his life. This work was supported by the NSFC (61571220, 61462052, 61502226 and 61601362).
Copyright information: © 2018 Elsevier B.V. All rights reserved. This manuscript version is made available under the CC-BY-NC-ND 4.0 license