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A generalized uncertainty principle and sparse representation in pairs of bases
Abstract
An elementary proof of a basic uncertainty principle concerning pairs of representations of R/sup N/ vectors in different orthonormal bases is provided. The result, slightly stronger than stated before, has a direct impact on the uniqueness property of the sparse representation of such vectors using pairs of orthonormal bases as overcomplete dictionaries. The main contribution in this paper is the improvement of an important result due to Donoho and Huo (2001) concerning the replacement of the l/sub 0/ optimization problem by a linear programming (LP) minimization when searching for the unique sparse representation.
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Citations
Cited by
Donoho, D. L. (2006) · IEEE Transactions on Information Theory · doi:10.1109/tit.2006.871582 · Cited by 23,994
Candes, E. J., Romberg, J., & Tao, T. (2006) · IEEE Transactions on Information Theory · doi:10.1109/tit.2005.862083 · Cited by 15,639
A sparse signal reconstruction perspective for source localization with sensor arrays
Malioutov, D., Cetin, M., & Willsky, A. S. (2005) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2005.850882 · Cited by 2,638
Global and local uncertainty principles for signals on graphs
Perraudin, N., Ricaud, B., Shuman, D. I., & Vandergheynst, P. (2018) · APSIPA Transactions on Signal and Information Processing · doi:10.1017/atsip.2018.2 · Cited by 58
Sparsity-Aware Learning and Compressed Sensing: An Overview
Theodoridis, S., Kopsinis, Y., & Slavakis, K. (2014) · Academic Press Library in Signal Processing · doi:10.1016/b978-0-12-396502-8.00023-1 · Cited by 14
Metadata
- Authors
- Elad, M., & Bruckstein, A. M.
- Venue
- IEEE Transactions on Information Theory
- Published
- 2002-09
- Volume
- 48
- Issue
- 9
- Pages
- 2558-2567
- ISSN
- 0018-9448 (ISSN-L)
- OpenAlex
- W2167839759
- Cited by
- 673
- References
- 0
- FWCI
- 23.59
- Type
- journal article
- Language
- en
- Open access
- closed
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