Abstract

Much research has recently been devoted to sparse signal recovery and image reconstruction from multiple measurement vectors. The assumption that the underlying signals or images have some common features with sparse representation suggests that using a joint sparsity approach to recover each individual signal or image can be more effective than recovering each signal or image separately using standard sparse recovery techniques. Joint sparsity reconstruction is typically performed using $\ell^{2,1}$-minimization, and although the process yields better results than separate recoveries, the inherent coupling makes the algorithm computationally intensive, since it is difficult to parallelize. In this investigation, we first observe that the elementwise variance of the signals convey information about their shared support. This observation motivates us to introduce a weighted $\ell^{1}$-joint sparsity algorithm, where the weights depend on the calculated variance. Specifically, the $\ell^1$-minimization should be more heavily penalized in regions where the corresponding variance is small, since it is likely there is no signal there. We demonstrate that our new method, which we refer to as variance-based joint sparse recovery, is more accurate and cost efficient. Applications in sparse signal recovery, parallel magnetic resonance imaging, and edge detection are considered.

Keywords

  1. sparse signal recovery
  2. multiple measurement vectors
  3. joint sparsity
  4. variance

MSC codes

  1. 65F22
  2. 65K10

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Information & Authors

Information

Published In

cover image SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Pages: A246 - A268
ISSN (online): 1095-7197

History

Submitted: 8 November 2017
Accepted: 19 November 2018
Published online: 10 January 2019

Keywords

  1. sparse signal recovery
  2. multiple measurement vectors
  3. joint sparsity
  4. variance

MSC codes

  1. 65F22
  2. 65K10

Authors

Affiliations

Funding Information

Alfred P. Sloan Foundation https://doi.org/10.13039/100000879
Air Force Office of Scientific Research https://doi.org/10.13039/100000181 : FA9550-18-1-0316, FA9550-15-1-0152
Natural Sciences and Engineering Research Council of Canada https://doi.org/10.13039/501100000038 : 611675
National Natural Science Foundation of China https://doi.org/10.13039/501100001809 : 11701383
National Science Foundation https://doi.org/10.13039/100000001 : DMS 1521661, DMS 1502640, DMS 1732434

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