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# Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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# Sparse signal recovery with prior information by iterative reweighted least squares algorithm

Nianci Feng
/ Jianjun Wang
/ Wendong Wang
Published Online: 2017-07-06 | DOI: https://doi.org/10.1515/jiip-2016-0087

## Abstract

In this paper, the iterative reweighted least squares (IRLS) algorithm for sparse signal recovery with partially known support is studied. We establish a theoretical analysis of the IRLS algorithm by incorporating some known part of support information as a prior, and obtain the error estimate and convergence result of this algorithm. Our results show that the error bound depends on the best $\left(s+k\right)$-term approximation and the regularization parameter λ, and convergence result depends only on the regularization parameter λ. Finally, a series of numerical experiments are carried out to demonstrate the effectiveness of the algorithm for sparse signal recovery with partially known support, which shows that an appropriate q ($0) can lead to a better recovery performance than that of the case $q=1$.

MSC 2010: 49M05; 65B99; 65K10; 90C26

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## About the article

Revised: 2017-05-25

Accepted: 2017-06-23

Published Online: 2017-07-06

Published in Print: 2018-04-01

Natural Science Foundation of China under Grant number 61273020, 61673015, Fundamental Research Funds for the Central Universities under Grant number XDJK2015A007.

Citation Information: Journal of Inverse and Ill-posed Problems, Volume 26, Issue 2, Pages 171–184, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219,

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