Multiscale Dictionary Learning via Cross-Scale Cooperative Learning and Atom Clustering for Visual Signal Processing

For sparse signal representation, the sparsity across the scales is a promising yet underinvestigated direction. In this paper, we aim to design a multiscale sparse representation scheme to explore such potential. A multiscale dictionary (MD) structure is designed. A cross-scale matching pursuit algorithm is proposed for multiscale sparse coding. Two dictionary learning methods, cross-scale cooperative learning and cross-scale atom clustering, are proposed each focusing on one of the two important attributes of an efficient MD: the similarity and uniqueness of corresponding atoms in different scales. We analyze and compare their different advantages in the application of image denoising under different noise levels, where both methods produce state-of-the-art denoising results.