Learning Multiscale Sparse Representations for Image and Video Restoration

Abstract : A framework for learning multiscale sparse representations of color images and video with over complete dictionaries is presented in this paper. Following the single-scale grayscale K-SVD algorithm introduced in [1], which formulates the sparse dictionary learning and image representation as an optimization problem efficiently solved via orthogonal matching pursuit and SVD, this proposed multiscale learned representation is obtained based on an efficient quadtree decomposition of the learned dictionary and overlapping image patches. The proposed framework provides an alternative to pre-defined dictionaries such as wavelets, and leads to state-of-the-art results in a number of image and video enhancement and restoration applications. The presentation of the framework here proposed is accompanied by numerous examples demonstrating its practical power.