Vector approximate message passing algorithm for compressed sensing with structured matrix perturbation

•Study the CS with structured matrix perturbation via Bayesian methods.•Develop the perturbation considered vector approximate message passing (PC-VAMP) algorithm.•Show the excellent performance of PC-VAMP. In this paper, we consider a general form of noisy compressive sensing (CS) where the sensing...

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Bibliographic Details
Published in:Signal processing Vol. 166; p. 107248
Main Authors: Zhu, Jiang, Zhang, Qi, Meng, Xiangming, Xu, Zhiwei
Format: Journal Article
Language:English
Published: Elsevier B.V 01.01.2020
Subjects:
Compressed sensing
Structured perturbation
VAMP
VAMP
Compressed sensing
Structured perturbation
ISSN:0165-1684, 1872-7557
Online Access:Get full text
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Summary:•Study the CS with structured matrix perturbation via Bayesian methods.•Develop the perturbation considered vector approximate message passing (PC-VAMP) algorithm.•Show the excellent performance of PC-VAMP. In this paper, we consider a general form of noisy compressive sensing (CS) where the sensing matrix is not precisely known. Such cases exist when there are imperfections or unknown calibration parameters during the measurement process. Particularly, the sensing matrix may have some structure, which makes the perturbation follow a fixed pattern. Previous work has focused on extending the approximate message passing (AMP) and LASSO algorithm to deal with the independent and identically distributed (i.i.d.) perturbation. Based on the recent VAMP algorithm, we take the structured perturbation into account and propose the perturbation considered vector approximate message passing (PC-VAMP) algorithm. Numerical results demonstrate the effectiveness of PC-VAMP.
ISSN:0165-1684
1872-7557
DOI:10.1016/j.sigpro.2019.107248