The Analysis Sparse Model - Definition, Pursuit, Dictionary Learning, and Beyond (Short-Version)
May, 2012
SIAM Imaging Science Conference, Philadelphia

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. While the two alternative models seem to be very close and similar, they are in fact very different. In this talk we define clearly the analysis model and describe how to generate signals from it. We discuss the pursuit denoising problem that seeks the zeros of the signal with respect to the analysis dictionary given noisy measurements. Finally, we explore ideas for learning the analysis dictionary from a set of signal examples. We demonstrate this model’s effectiveness in several experiments, treating synthetic data and real images, showing a successful and meaningful recovery of the analysis dictionary.

This is a short-version of the talk below. It was given as an invited talk in the SIAM Imaging Science Conference, in the Session "Sparse and Redundant Representations for Image Reconstruction and Geometry Extraction", organized by Weihong Guo (Case Western Reserve University, USA), Philadelphia May 2012. This talk was also given in a Machine-Learning Workshop in Janelia Farm (May, 2012). Joint work with Ron Rubinstein (former PhD student), Tomer Faktor (PhD student), Remi Gribonval and Sangnam Nam (INRIA, Rennes), and Mike Davies (UEdin).