A Generalized Iterated Shrinkage Algorithm for Non-convex Sparse Coding

Wangmeng Zuo, Deyu Meng, Lei Zhang, Xiangchu Feng, David Zhang; The IEEE International Conference on Computer Vision (ICCV), 2013, pp. 217-224

Abstract


In many sparse coding based image restoration and image classification problems, using non-convex p -norm minimization (0 top po1) can often obtain better results than the convex 1 -norm minimization. A number of algorithms, e.g., iteratively reweighted least squares (IRLS), iteratively thresholding method (ITMp ), and look-up table (LUT), have been proposed for non-convex p -norm sparse coding, while some analytic solutions have been suggested for some specific values of p. In this paper, by extending the popular soft-thresholding operator, we propose a generalized iterated shrinkage algorithm (GISA) for p -norm non-convex sparse coding. Unlike the analytic solutions, the proposed GISA algorithm is easy to implement, and can be adopted for solving non-convex sparse coding problems with arbitrary p values. Compared with LUT, GISA is more general and does not need to compute and store the look-up tables. Compared with IRLS and ITMp , GISA is theoretically more solid and can achieve more accurate solutions. Experiments on image restoration and sparse coding based face recognition are conducted to validate the performance of GISA.

Related Material


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[bibtex]
@InProceedings{Zuo_2013_ICCV,
author = {Zuo, Wangmeng and Meng, Deyu and Zhang, Lei and Feng, Xiangchu and Zhang, David},
title = {A Generalized Iterated Shrinkage Algorithm for Non-convex Sparse Coding},
booktitle = {The IEEE International Conference on Computer Vision (ICCV)},
month = {December},
year = {2013}
}