학술논문
Relaxed Recovery Conditions for OMP/OLS by Exploiting Both Coherence and Decay
Document Type
Periodical
Author
Source
IEEE Transactions on Information Theory IEEE Trans. Inform. Theory Information Theory, IEEE Transactions on. 62(1):459-470 Jan, 2016
Subject
Language
ISSN
0018-9448
1557-9654
1557-9654
Abstract
We propose extended coherence-based conditions for exact sparse support recovery using orthogonal matching pursuit and orthogonal least squares. Unlike standard uniform guarantees, we embed some information about the decay of the sparse vector coefficients in our conditions. As a result, the standard condition $\mu (where $\mu $ denotes the mutual coherence and $k$ the sparsity level) can be weakened as soon as the nonzero coefficients obey some decay, both in the noiseless and the bounded-noise scenarios. Furthermore, the resulting condition is approaching $\mu for strongly decaying sparse signals. Finally, in the noiseless setting, we prove that the proposed conditions, in particular the bound $\mu , are the tightest achievable guarantees based on mutual coherence.