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Orthogonal Greedy MUSIC: An Empirical Algorithm for Joint Sparse Recovery

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Abstract

This paper addresses the multiple measurement vector problem, which aims at recovering jointly sparse vectors from incomplete measurements. Inspired by MUSIC (MUltiple SIgnal Classification) and the greedy algorithms used in compressed sensing, we propose an empirical algorithm, called orthogonal greedy MUSIC (OG-MUSIC), for solving the problem. The proposed algorithm is a greedy algorithm, and a MUSIC procedure and an orthogonal projection operation are applied in each iteration. Since MUSIC is used in each iteration, multiple support elements may be selected per iteration; this is one of the main advantages of OG-MUSIC. The other main advantage of OG-MUSIC is the pruning technique, which is used to find the exact row support when the merged support size is larger than the sparsity level. Theoretical analysis and simulation results illustrate that OG-MUSIC has a very good recovery performance while maintaining a relatively low computational cost.

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Acknowledgements

We appreciate the anonymous reviewers’ constructive comments, which have greatly improved this paper. The work is supported in part by the National Natural Science Foundation of China under grants 61271014, 11101430, and 61072118, and by the ATR National Defense Technology Key Laboratory Foundation under grant 11ZS93.

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Authors and Affiliations

  1. Department of Mathematics and System Science, College of Science, National University of Defense Technology, Changsha, 410073, China

    Xinpeng Du, Ruihua Liang, Lizhi Cheng & Fang Su

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  1. Xinpeng Du
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  2. Ruihua Liang
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  3. Lizhi Cheng
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  4. Fang Su
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Correspondence to Xinpeng Du.

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Du, X., Liang, R., Cheng, L. et al. Orthogonal Greedy MUSIC: An Empirical Algorithm for Joint Sparse Recovery. Circuits Syst Signal Process 32, 3079–3091 (2013). https://doi.org/10.1007/s00034-013-9616-1

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  • DOI: https://doi.org/10.1007/s00034-013-9616-1

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