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The Sufficient Conditions for Orthogonal Matching Pursuit to Exactly Reconstruct Sparse Polynomials

Author

Listed:
  • Aitong Huang

    (School of Mathematics Science, Beihang University, Beijing 102200, China
    These authors contributed equally to this work.)

  • Renzhong Feng

    (School of Mathematics Science, Beihang University, Beijing 102200, China
    These authors contributed equally to this work.)

  • Andong Wang

    (School of Mathematics Science, Beihang University, Beijing 102200, China)

Abstract

Orthogonal matching pursuit (OMP for short) is a classical method for sparse signal recovery in compressed sensing. In this paper, we consider the application of OMP to reconstruct sparse polynomials generated by uniformly bounded orthonormal systems, which is an extension of the work on OMP to reconstruct sparse trigonometric polynomials. Firstly, in both cases of sampled data with and without noise, sufficient conditions for OMP to recover the coefficient vector of a sparse polynomial are given, which are more loose than the existing results. Then, based on a more accurate estimation of the mutual coherence of a structured random matrix, the recovery guarantees and success probabilities for OMP to reconstruct sparse polynomials are obtained with the help of those sufficient conditions. In addition, the error estimation for the recovered coefficient vector is gained when the sampled data contain noise. Finally, the validity and correctness of the theoretical conclusions are verified by numerical experiments.

Suggested Citation

  • Aitong Huang & Renzhong Feng & Andong Wang, 2022. "The Sufficient Conditions for Orthogonal Matching Pursuit to Exactly Reconstruct Sparse Polynomials," Mathematics, MDPI, vol. 10(19), pages 1-23, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3703-:d:937820
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    Cited by:

    1. Xu Xu & Jinyu Guo & Peixin Ye & Wenhui Zhang, 2023. "Approximation Properties of the Vector Weak Rescaled Pure Greedy Algorithm," Mathematics, MDPI, vol. 11(9), pages 1-23, April.

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