The Cosparse Analysis Model and Algorithms

TL;DR

This paper explores the analysis sparse model for signal representation, contrasting it with the synthesis model, and introduces algorithms and theoretical insights to improve its application in inverse problems.

Contribution

It provides a clearer definition of the analysis model, proposes effective pursuit algorithms, and offers initial theoretical analysis of their performance.

Findings

Analysis model can effectively regularize inverse problems.

Proposed algorithms show promising experimental results.

Theoretical insights support the analysis approach's viability.

Abstract

After a decade of extensive study of the sparse representation synthesis model, we can safely say that this is a mature and stable field, with clear theoretical foundations, and appealing applications. Alongside this approach, there is an analysis counterpart model, which, despite its similarity to the synthesis alternative, is markedly different. Surprisingly, the analysis model did not get a similar attention, and its understanding today is shallow and partial. In this paper we take a closer look at the analysis approach, better define it as a generative model for signals, and contrast it with the synthesis one. This work proposes effective pursuit methods that aim to solve inverse problems regularized with the analysis-model prior, accompanied by a preliminary theoretical study of their performance. We demonstrate the effectiveness of the analysis model in several experiments.