K-SVD Dictionary-Learning for Analysis Sparse Models
June 30th, 2011
SPARS11 - Workshop on signal processing with adaptive sparse structured representations.

The synthesis-based sparse representation model for signals has drawn a considerable interest in the past decade. Such a model assumes that the signal of interest can be decomposed as a linear combination of a  few atoms from a given dictionary. In this talk we concentrate on an alternative, analysis-based model, where an analysis operator — hereafter referred to as the “Analysis Dictionary” – multiplies the signal, leading to a sparse outcome. Our goal is to learn the analysis dictionary from a set of signal examples, and the approach taken is parallel and similar to the one adopted by the K-SVD algorithm that serves the corresponding problem in the synthesis model. We present the development of the algorithm steps, which include a tailored pursuit algorithm termed “Backward Greedy” algorithm and a penalty function for the dictionary update stage. We demonstrate its effectiveness in several experiments, treating synthetic data and real images, showing a successful and meaningful recovery of the analysis dictionary.

This is a joint work with Ron Rubinstein.