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Compressed Sensing and Redundant Dictionaries
Open accessAbstract
This paper extends the concept of compressed sensing to signals that are not sparse in an orthonormal basis but rather in a redundant dictionary. It is shown that a matrix, which is a composition of a random matrix of certain type and a deterministic dictionary, has small restricted isometry constants. Thus, signals that are sparse with respect to the dictionary can be recovered via basis pursuit (BP) from a small number of random measurements. Further, thresholding is investigated as recovery algorithm for compressed sensing, and conditions are provided that guarantee reconstruction with high probability. The different schemes are compared by numerical experiments.
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Cited by
Signal Processing With Compressive Measurements
Davenport, M. A., Boufounos, P. T., Wakin, M. B., & Baraniuk, R. G. (2010) · IEEE Journal of Selected Topics in Signal Processing · doi:10.1109/jstsp.2009.2039178 · Cited by 623
Huang, J., & Zhang, T. (2010) · The Annals of Statistics · doi:10.1214/09-aos778 · Cited by 521
Highly Undersampled Magnetic Resonance Image Reconstruction via Homotopic $\ell_{0}$-Minimization
Trzasko, J., & Manduca, A. (2009) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2008.927346 · Cited by 490
Duarte, M. F., & Baraniuk, R. G. (2013) · Applied and Computational Harmonic Analysis · doi:10.1016/j.acha.2012.08.003 · Cited by 428
Secure and Robust Iris Recognition Using Random Projections and Sparse Representations
Pillai, J. K., Patel, V. M., Chellappa, R., & Ratha, N. K. (2011) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2011.34 · Cited by 324
Metadata
- Authors
- Rauhut, H., Schnass, K., & Vandergheynst, P.
- Venue
- IEEE Transactions on Information Theory
- Published
- 2008-05
- Volume
- 54
- Issue
- 5
- Pages
- 2210-2219
- ISSN
- 0018-9448 (ISSN-L)
- OpenAlex
- W2105877514
- Cited by
- 541
- References
- 0
- FWCI
- 45.16
- Type
- journal article
- Language
- en
- Open access
- green
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