In this work, we study the cross-scale sparsity embeded within visual signals. A cleverly designed dictionary that aims at preverving visual signal’s scale-dependent similarity and uniquess shows effeciency in image denoising applications.
For sparse signal representation, the sparsity across the scales is a promising yet under investigated direction. In this work, we aim at designing a multi-scale sparse representation scheme to explore such potential. A multi-scale dictionary (MD) structure is designed. A Cross-scale Matching Pursuit (CMP) algorithm is proposed for multi-scale sparse coding. Two dictionary learning methods: Cross-scale Cooperative Learning MD/CCL), and Cross-scale Atom Clustering (MD/CAC) are proposed with each focusing on one of the two important attributes of an efficient multi-scale dictionary: 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 stateof-the-art denoising results.