- Title
- An improved smoothed ℓ⁰ approximation algorithm for sparse representation
- Creator
- Hyder, Md Mashud; Mahata, Kaushik
- Relation
- IEEE Transactions on Signal Processing Vol. 58, Issue 4, p. 2194-2205
- Publisher Link
- http://dx.doi.org/10.1109/tsp.2009.2040018
- Publisher
- Institute of Electrical and Electronics Engineers (IEEE)
- Resource Type
- journal article
- Date
- 2010
- Description
- ℓ⁰ norm based algorithms have numerous potential applications where a sparse signal is recovered from a small number of measurements. The direct ℓ⁰ norm optimization problem is P-hard. In this paper we work with the the smoothed ℓ⁰ (SL0) approximation algorithm for sparse representation. We give an upper bound on the run-time estimation error. This upper bound is tighter than the previously known bound. Subsequently, we develop a reliable stopping criterion. This criterion is helpful in avoiding the problems due to the underlying discontinuities of the ℓ⁰ cost function. Furthermore, we propose an alternative optimization strategy, which results in a Newton like algorithm.
- Subject
- basis pursuit; compressive sampling; ℓ¹-norm minimization; linear programming; nonconvex optimization; overcomplete representation; sparse representation
- Identifier
- http://hdl.handle.net/1959.13/927353
- Identifier
- uon:10121
- Identifier
- ISSN:1053-587X
- Rights
- Copyright © 2010 IEEE. Reprinted from IEEE Transactions on Signal Processing Vol. 58, Issue 4, p. 2194-2205. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Newcastle's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.
- Language
- eng
- Full Text
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