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2010•AIP conference proceedingsRequires access

Near-Oracle Performance Guarantees for Greedy-Like Methods

Raja Giryes, Michael Elad, Theodore E. Simos, George Psihoyios, Ch. Tsitouras

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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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What this paper is about

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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Available 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.

Key concepts: Matching pursuit, Computer science, Sparse approximation, Oracle, Restricted isometry property, Greedy algorithm, Compressed sensing, Thresholding

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