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- Title
The Sufficient Conditions for Orthogonal Matching Pursuit to Exactly Reconstruct Sparse Polynomials.
- Authors
Huang, Aitong; Feng, Renzhong; Wang, Andong
- 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.
- Subjects
ORTHOGONAL matching pursuit; POLYNOMIALS; COMPRESSED sensing; RANDOM matrices
- Publication
Mathematics (2227-7390), 2022, Vol 10, Issue 19, p3703
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math10193703