Close Search Advanced
Journals
Resources
About Us
Open Access

The Exact Recovery of Sparse Signals via Orthogonal Matching Pursuit

The Exact Recovery of Sparse Signals via Orthogonal Matching Pursuit
Preview
Add to basket

Year:    2016

Author:    Anping Liao, Jiaxin Xie, Xiaobo Yang, Peng Wang

Journal of Computational Mathematics, Vol. 34 (2016), Iss. 1 : pp. 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.

Submit Article

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1510-m2015-0284

Journal of Computational Mathematics, Vol. 34 (2016), Iss. 1 : pp. 70–86

Published online:    2016-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    17

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

Author Details

Anping Liao

Jiaxin Xie

Xiaobo Yang

Peng Wang

  1. New Conditions on Stable Recovery of Weighted Sparse Signals via Weighted $$l_1$$ l 1 Minimization

    Huo, Haiye | Sun, Wenchang | Xiao, Li

    Circuits, Systems, and Signal Processing, Vol. 37 (2018), Iss. 7 P.2866

    https://doi.org/10.1007/s00034-017-0691-6 [Citations: 4]

  2. Orthogonal Least Squares Detector for Generalized Spatial Modulation

    Wen, Jinming | Li, Jie | Ge, Huanmin | Zhou, Zhengchun | Luo, Weiqi

    IEEE Transactions on Wireless Communications, Vol. 20 (2021), Iss. 8 P.5071

    https://doi.org/10.1109/TWC.2021.3065383 [Citations: 3]

  3. Theoretical analysis of GOMP based on RIP and ROC

    Li, Haifeng | Guo, Leiyan

    Japan Journal of Industrial and Applied Mathematics, Vol. 41 (2024), Iss. 2 P.1277

    https://doi.org/10.1007/s13160-024-00651-9 [Citations: 0]