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Improved optimization algorithm for proximal point-based dictionary updating methods

[+] Author Affiliations
Changchen Zhao

National Chung Hsing University, Department of Electrical Engineering, 145 Xingda Road, South District, Taichung City 402, Taiwan

Beihang University, School of Automation Science and Electrical Engineering, 37 Xueyuan Road, Haidian District, Beijing 100191, China

Wen-Liang Hwang

National Chung Hsing University, Department of Electrical Engineering, 145 Xingda Road, South District, Taichung City 402, Taiwan

Academia Sinica, Institute of Information Science, 128 Academia Road, Section 2, Nankang, Taipei 11529, Taiwan

Chun-Liang Lin

National Chung Hsing University, Department of Electrical Engineering, 145 Xingda Road, South District, Taichung City 402, Taiwan

Weihai Chen

Beihang University, School of Automation Science and Electrical Engineering, 37 Xueyuan Road, Haidian District, Beijing 100191, China

J. Electron. Imaging. 25(5), 053036 (Oct 25, 2016). doi:10.1117/1.JEI.25.5.053036
History: Received April 27, 2016; Accepted October 3, 2016
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Abstract.  Proximal K-singular value decomposition (PK-SVD) is a dictionary updating algorithm that incorporates proximal point method into K-SVD. The attempt of combining proximal method and K-SVD has achieved promising result in such areas as sparse approximation, image denoising, and image compression. However, the optimization procedure of PK-SVD is complicated and, therefore, limits the algorithm in both theoretical analysis and practical use. This article proposes a simple but effective optimization approach to the formulation of PK-SVD. We cast this formulation as a fitting problem and relax the constraint on the direction of the k’th row in the sparse coefficient matrix. This relaxation strengthens the regularization effect of the proximal point. The proposed algorithm needs fewer steps to implement and further boost the performance of PK-SVD while maintaining the same computational complexity. Experimental results demonstrate that the proposed algorithm outperforms conventional algorithms in reconstruction error, recovery rate, and convergence speed for sparse approximation and achieves better results in image denoising.

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Citation

Changchen Zhao ; Wen-Liang Hwang ; Chun-Liang Lin and Weihai Chen
"Improved optimization algorithm for proximal point-based dictionary updating methods", J. Electron. Imaging. 25(5), 053036 (Oct 25, 2016). ; http://dx.doi.org/10.1117/1.JEI.25.5.053036


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