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Volume 34, Issue 1
The Exact Recovery of Sparse Signals via Orthogonal Matching Pursuit

Anping Liao, Jiaxin Xie, Xiaobo Yang & Peng Wang

DOI: 10.4208/jcm.1510-m2015-0284

J. Comp. Math., 34 (2016), pp. 70-86.

Published online: 2016-02

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  • Abstract

This paper aims to investigate sufficient conditions for the recovery of sparse signals via the orthogonal matching pursuit (OMP) algorithm. In the noiseless case, we present a novel sufficient condition for the exact recovery of all $k$-sparse signals by the OMP algorithm, and demonstrate that this condition is sharp. In the noisy case, a sufficient condition for recovering the support of $k$-sparse signal is also presented. Generally, the computation for the restricted isometry constant (RIC) in these sufficient conditions is typically difficult, therefore we provide a new condition which is not only computable but also sufficient for the exact recovery of all $k$-sparse signals.

  • Keywords

Compressed sensing, Sparse signal recovery, Restricted orthogonality constant (ROC), Restricted isometry constant (RIC), Orthogonal matching pursuit (OMP).

  • AMS Subject Headings

90C90, 94A12, 65J22, 15A29.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

liaoap@hnu.edu.cn (Anping Liao)

xiejiaxin@hnu.edu.cn (Jiaxin Xie)

xiaoboyang@hnu.edu.cn (Xiaobo Yang)

p_wong@126.com (Peng Wang)

  • BibTex
  • RIS
  • TXT
@Article{JCM-34-70, author = {Liao , AnpingXie , JiaxinYang , Xiaobo and Wang , Peng}, title = {The Exact Recovery of Sparse Signals via Orthogonal Matching Pursuit}, journal = {Journal of Computational Mathematics}, year = {2016}, volume = {34}, number = {1}, pages = {70--86}, abstract = {

This paper aims to investigate sufficient conditions for the recovery of sparse signals via the orthogonal matching pursuit (OMP) algorithm. In the noiseless case, we present a novel sufficient condition for the exact recovery of all $k$-sparse signals by the OMP algorithm, and demonstrate that this condition is sharp. In the noisy case, a sufficient condition for recovering the support of $k$-sparse signal is also presented. Generally, the computation for the restricted isometry constant (RIC) in these sufficient conditions is typically difficult, therefore we provide a new condition which is not only computable but also sufficient for the exact recovery of all $k$-sparse signals.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1510-m2015-0284}, url = {http://global-sci.org/intro/article_detail/jcm/9783.html} }
TY - JOUR T1 - The Exact Recovery of Sparse Signals via Orthogonal Matching Pursuit AU - Liao , Anping AU - Xie , Jiaxin AU - Yang , Xiaobo AU - Wang , Peng JO - Journal of Computational Mathematics VL - 1 SP - 70 EP - 86 PY - 2016 DA - 2016/02 SN - 34 DO - http://doi.org/10.4208/jcm.1510-m2015-0284 UR - https://global-sci.org/intro/article_detail/jcm/9783.html KW - Compressed sensing, Sparse signal recovery, Restricted orthogonality constant (ROC), Restricted isometry constant (RIC), Orthogonal matching pursuit (OMP). AB -

This paper aims to investigate sufficient conditions for the recovery of sparse signals via the orthogonal matching pursuit (OMP) algorithm. In the noiseless case, we present a novel sufficient condition for the exact recovery of all $k$-sparse signals by the OMP algorithm, and demonstrate that this condition is sharp. In the noisy case, a sufficient condition for recovering the support of $k$-sparse signal is also presented. Generally, the computation for the restricted isometry constant (RIC) in these sufficient conditions is typically difficult, therefore we provide a new condition which is not only computable but also sufficient for the exact recovery of all $k$-sparse signals.

Liao , AnpingXie , JiaxinYang , Xiaobo and Wang , Peng. (2016). The Exact Recovery of Sparse Signals via Orthogonal Matching Pursuit. Journal of Computational Mathematics. 34 (1). 70-86. doi:10.4208/jcm.1510-m2015-0284
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