Near-oracle performance guarantees for greedy-like methods

Raja Giryes; Michael Elad

doi:10.1063/1.3498194

Near-oracle performance guarantees for greedy-like methods

Raja Giryes^*, Michael Elad

^*Corresponding author for this work

Technion-Israel Institute of Technology

Research output: Contribution to journal › Conference article › peer-review

Abstract

In this paper analysis for Greedy-Like methods are presented. These methods include Subspace Pursuit (SP), Compressive Sampling Matching Pursuit (CoSaMP) and Iterative Hard Thresholding (IHT) algorithms. The proposed analysis is based on the Restricted-Isometry-Property (RIP), establishing a near-oracle performance guarantee for each of these techniques. The signal is assumed to be corrupted by an additive random white Gaussian noise; and to have a K-sparse representation with respect to a known dictionary D. The results for the three algorithms are of the same type but uses different constants and different requirements on the cardinality of the sparse representation.

Original language	English
Pages (from-to)	1734-1736
Number of pages	3
Journal	AIP Conference Proceedings
Volume	1281
DOIs	https://doi.org/10.1063/1.3498194
State	Published - 2010
Externally published	Yes
Event	International Conference on Numerical Analysis and Applied Mathematics 2010, ICNAAM-2010 - Rhodes, Greece Duration: 19 Sep 2010 → 25 Sep 2010

Keywords

CoSaMP
Compressed Sensing
Iterative Hard Thresholding
Near Oracle performance
Subspace Pursuit

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10.1063/1.3498194

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abstract = "In this paper analysis for Greedy-Like methods are presented. These methods include Subspace Pursuit (SP), Compressive Sampling Matching Pursuit (CoSaMP) and Iterative Hard Thresholding (IHT) algorithms. The proposed analysis is based on the Restricted-Isometry-Property (RIP), establishing a near-oracle performance guarantee for each of these techniques. The signal is assumed to be corrupted by an additive random white Gaussian noise; and to have a K-sparse representation with respect to a known dictionary D. The results for the three algorithms are of the same type but uses different constants and different requirements on the cardinality of the sparse representation.",

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AU - Elad, Michael

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AB - In this paper analysis for Greedy-Like methods are presented. These methods include Subspace Pursuit (SP), Compressive Sampling Matching Pursuit (CoSaMP) and Iterative Hard Thresholding (IHT) algorithms. The proposed analysis is based on the Restricted-Isometry-Property (RIP), establishing a near-oracle performance guarantee for each of these techniques. The signal is assumed to be corrupted by an additive random white Gaussian noise; and to have a K-sparse representation with respect to a known dictionary D. The results for the three algorithms are of the same type but uses different constants and different requirements on the cardinality of the sparse representation.

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Near-oracle performance guarantees for greedy-like methods

Abstract

Keywords

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