The cosparse analysis model and algorithms

S. Nam, M. E. Davies, M. Elad, R. Gribonval

Research output: Contribution to journalArticlepeer-review

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, and provide a detailed study of the model associated with the 2D finite difference analysis operator, a close cousin of the TV norm.

Original languageEnglish
Pages (from-to)30-56
Number of pages27
JournalApplied and Computational Harmonic Analysis
Volume34
Issue number1
DOIs
StatePublished - Jan 2013

Keywords

  • Analysis
  • Compressed-sensing
  • Greedy algorithms
  • Pursuit algorithms
  • Sparse representations
  • Synthesis
  • Union of subspaces

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

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