The DOI matches its Crossref record; 39 of the 39 references it cites were found in a registry or an index.
The cosparse analysis model and algorithms
Open accessAbstract
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.
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Cites
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$rm K$-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation
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Self-citationMatching pursuits with time-frequency dictionaries
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Atomic Decomposition by Basis Pursuit
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Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries
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Self-citationThe contourlet transform: an efficient directional multiresolution image representation
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Greed is Good: Algorithmic Results for Sparse Approximation
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Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ 1 minimization
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Cited by
Sparse Regularization via Convex Analysis
Selesnick, I. (2017) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2017.2711501 · Cited by 429
Zhou, N., Jiang, H., Gong, L., & Xie, X. (2018) · Optics and Lasers in Engineering · doi:10.1016/j.optlaseng.2018.05.014 · Cited by 132
Metadata
- Authors
- Nam, S., Davies, M. E., Elad, M., & Gribonval, R.
- Venue
- Applied and Computational Harmonic Analysis
- Publisher
- Elsevier BV
- Published
- 2013-01
- Volume
- 34
- Issue
- 1
- Pages
- 30-56
- ISSN
- 1063-5203 (ISSN-L)
- OpenAlex
- W2152171106
- Cited by
- 353
- References
- 39
- FWCI
- 32.09
- Type
- journal article
- Language
- en
- Open access
- bronze
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