Alternating projection for sparse recovery

Reconstructing the sparse signal from a few linear measurements has attracted increasing attentions in recent years. In this study, the authors propose the alternating projection (AP) method for sparse signal recovery with learning the sparsity of the original signal. Different with classical hard t...

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Vydáno v:	IET signal processing Ročník 11; číslo 2; s. 135 - 144
Hlavní autoři:	Sun, Tao, Du, Peibing, Cheng, Lizhi, Jiang, Hao
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	The Institution of Engineering and Technology 01.04.2017
Témata:	Algorithms alternating projection method AP method classical hard thresholding algorithms Efficiency images reconstruction intersect point Learning linear measurements Mathematical models matrix algebra Noise noise‐robust algorithm Projection Research Article sensing matrix Signal processing Signal reconstruction sparse recovery sparse signal reconstruction s‐sparse linear measurements alternating projection method sparse signal reconstruction sparse recovery classical hard thresholding algorithms s-sparse matrix algebra sensing matrix images reconstruction noise-robust algorithm signal reconstruction intersect point AP method
ISSN:	1751-9675, 1751-9683, 1751-9683
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Shrnutí:	Reconstructing the sparse signal from a few linear measurements has attracted increasing attentions in recent years. In this study, the authors propose the alternating projection (AP) method for sparse signal recovery with learning the sparsity of the original signal. Different with classical hard thresholding algorithms, the AP method regards the signal recovery problem as finding an intersect point of two sets. Theoretically, the authors prove that the proposed algorithm can reconstruct the s-sparse original signal provided the sensing matrix satisfies several assumptions when the noise is absent. They also prove that AP method is a noise-robust algorithm, i.e. a tolerable reconstruction can be obtained by AP if the noise is small. In numerical experiments, the authors compare AP with several existing algorithms when being applied to sparse signals recovery and images reconstruction. The results demonstrate the efficiency of the proposed algorithm.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23
ISSN:	1751-9675 1751-9683 1751-9683
DOI:	10.1049/iet-spr.2016.0020