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

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Published/Copyright: July 6, 2017
Journal of Inverse and Ill-posed Problems
From the journal Journal of Inverse and Ill-posed Problems Volume 26 Issue 2

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 (s+k)-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<q<1) can lead to a better recovery performance than that of the case q=1.

Keywords: Compressed sensing; sparsity; prior information; iterative reweighted least squares algorithm
MSC 2010: 49M05; 65B99; 65K10; 90C26

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

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Received: 2017-1-18
Revised: 2017-5-25
Accepted: 2017-6-23
Published Online: 2017-7-6
Published in Print: 2018-4-1

© 2018 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

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  2. A parameter choice strategy for a multilevel augmentation method in iterated Lavrentiev regularization
  3. Sparse signal recovery with prior information by iterative reweighted least squares algorithm
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https://doi.org/10.1515/jiip-2016-0087
Keywords for this article
Compressed sensing; sparsity; prior information; iterative reweighted least squares algorithm

Articles in the same Issue

  1. Frontmatter
  2. A parameter choice strategy for a multilevel augmentation method in iterated Lavrentiev regularization
  3. Sparse signal recovery with prior information by iterative reweighted least squares algorithm
  4. Towards dynamic PET reconstruction under flow conditions: Parameter identification in a PDE model
  5. Simultaneous determination of the magnetic field and the electric potential in the Schrödinger equation by a finite number of boundary observations
  6. Frechet differentiability in Besov spaces in the optimal control of parabolic free boundary problems
  7. Data-driven multichannel seismic impedance inversion with anisotropic total variation regularization
  8. Full waveform inversion with sparse structure constrained regularization
  9. Marching schemes for Cauchy wave propagation problems in laterally varying waveguides
  10. Existence of variational source conditions for nonlinear inverse problems in Banach spaces
  11. On ill-posedness concepts, stable solvability and saturation
  12. A linear algorithm for the identification of a weakly singular relaxation kernel using two boundary measurements
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