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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Bibliographic Details
Published in:IET signal processing Vol. 11; no. 2; pp. 135 - 144
Main Authors: Sun, Tao, Du, Peibing, Cheng, Lizhi, Jiang, Hao
Format: Journal Article
Language:English
Published: The Institution of Engineering and Technology 01.04.2017
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:1751-9675
1751-9683
1751-9683
DOI:10.1049/iet-spr.2016.0020