K-SVD dictionary-learning for the analysis sparse model

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 paper we concentrate on an alternative, analysis-based model, where an Analysis Dictionary multiplies the signal, leading to a sparse out-come. 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 two greedy tailored pursuit algorithms and a penalty function for the dictionary update stage. We demonstrate its effectiveness in several experiments, showing a successful and meaningful recovery of the analysis dictionary.