Multiscale sparse image representation with learned dictionaries

This paper introduces a new framework for learning multiscale sparse representations of natural images with overcomplete dictionaries. Our work extends the K-SVD algorithm [1], which learns sparse single-scale dictionaries for natural images. Recent work has shown that the K-SVD can lead to state-of-the-art image restoration results [2, 3]. We show that these are further improved with a multiscale approach, based on a Quadtree decomposition. Our framework provides an alternative to multiscale pre-defined dictionaries such as wavelets, curvelets, and contourlets, with dictionaries optimized for the data and application instead of pre-modelled ones.