A Generalized Iterated Shrinkage Algorithm for Non-convex Sparse Coding

In many sparse coding based image restoration and image classification problems, using non-convex l(p)-norm minimization (0 <= p < 1) can often obtain better results than the convex l(1)-norm minimization. A number of algorithms, e.g., iteratively reweighted least squares (IRLS), iteratively thresholding method (ITM-l(p)), and look-up table (LUT), have been proposed for non-convex l(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 l(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 ITM-l(p), 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.