25 October 2016 Improved optimization algorithm for proximal point-based dictionary updating methods
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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.
Changchen Zhao, Changchen Zhao, Wen-Liang Hwang, Wen-Liang Hwang, Chun-Liang Lin, Chun-Liang Lin, Weihai Chen, Weihai Chen, } "Improved optimization algorithm for proximal point-based dictionary updating methods," Journal of Electronic Imaging 25(5), 053036 (25 October 2016). https://doi.org/10.1117/1.JEI.25.5.053036 . Submission:

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