Sparse dictionary learning by block proximal gradient with global convergence

摘要

The present paper focuses on dictionary learning in the double sparsity model for sparse representation (or approximation). Due to the highly non-convexity and discontinuity of l(0) pseudo-norm, the proofs of convergence for sparse K singular value decomposition (Sparse-KSVD) and online sparse dictionary learning (OSDL) are challenging. To theoretically analyze the convergence, we relax the l(0) pseudo-norm to the convex entry-wise l(1) norm, and reformulate the constrained optimization problem as an unconstrained one leveraging the double-l(1)-regularizer. Therefore, the problem becomes bi-convex. To train a sparse dictionary, an algorithm based on the block proximal gradient (BPG) framework with global convergence is derived. Several experiments are presented to show that our algorithm outperforms Sparse-KSVD and OSDL in some cases. (C) 2019 Elsevier B.V. All rights reserved.