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Sharp sufficient conditions for stable recovery of block sparse signals by block orthogonal matching pursuit.
- Source :
-
Applied & Computational Harmonic Analysis . Nov2019, Vol. 47 Issue 3, p948-974. 27p. - Publication Year :
- 2019
-
Abstract
- In this paper, we use the block orthogonal matching pursuit (BOMP) algorithm to recover block sparse signals x from measurements y = A x + v , where v is an ℓ 2 -bounded noise vector (i.e., ‖ v ‖ 2 ≤ ϵ for some constant ϵ). We investigate some sufficient conditions based on the block restricted isometry property (block-RIP) for exact (when v = 0) and stable (when v ≠ 0) recovery of block sparse signals x . First, on the one hand, we show that if A satisfies the block-RIP with δ K + 1 < 1 / K + 1 , then every block K -sparse signal x can be exactly or stably recovered by BOMP in K iterations. On the other hand, we show that, for any K ≥ 1 and 1 / K + 1 ≤ δ < 1 , there exists a matrix A satisfying the block-RIP with δ K + 1 = δ and a block K -sparse signal x such that BOMP may fail to recover x in K iterations. Then, we study some sufficient conditions for recovering block α -strongly-decaying K -sparse signals. We show that if A satisfies the block-RIP with δ K + 1 < 2 / 2 , then every α -strongly-decaying block K -sparse signal can be exactly or stably recovered by BOMP in K iterations under some conditions on α. Our newly found sufficient condition on the block-RIP of A is less restrictive than that for ℓ 1 minimization for this special class of sparse signals. Furthermore, for any K ≥ 1 , α > 1 and 2 / 2 ≤ δ < 1 , the recovery of x may fail in K iterations for a sensing matrix A which satisfies the block-RIP with δ K + 1 = δ. Finally, we study some sufficient conditions for partial recovery of block sparse signals. Specifically, if A satisfies the block-RIP with δ K + 1 < 2 / 2 , then BOMP is guaranteed to recover some blocks of x if these blocks satisfy a sufficient condition. We further show that this condition is also sharp. [ABSTRACT FROM AUTHOR]
- Subjects :
- *ORTHOGONAL matching pursuit
*COMPRESSED sensing
Subjects
Details
- Language :
- English
- ISSN :
- 10635203
- Volume :
- 47
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Applied & Computational Harmonic Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 138156367
- Full Text :
- https://doi.org/10.1016/j.acha.2018.02.002