A non-convex relaxation approach to sparse dictionary learning

Dictionary learning is a challenging theme in computer vision. The basic goal is to learn a sparse representation from an overcomplete basis set. Most existing approaches employ a convex relaxation scheme to tackle this challenge due to the strong ability of convexity in computation and theoretical analysis. In this paper we propose a non-convex online approach for dictionary learning. To achieve the sparseness, our approach treats a so-called minimax concave (MC) penalty as a nonconvex relaxation of the ℓ
₀
penalty. This treatment expects to obtain a more robust and sparse representation than existing convex approaches. In addition, we employ an online algorithm to adaptively learn the dictionary, which makes the non-convex formulation computationally feasible. Experimental results on the sparseness comparison and the applications in image denoising and image inpainting demonstrate that our approach is more effective and flexible.