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Relaxed Recovery Conditions for OMP/OLS by Exploiting both Coherence and Decay
We propose extended coherence-based conditions for exact sparse support
recovery using orthogonal matching pursuit (OMP) and orthogonal least squares
(OLS). 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 (where denotes the mutual coherence and
the sparsity level) can be weakened as soon as the non-zero coefficients
obey some decay, both in the noiseless and the bounded-noise scenarios.
Furthermore, the resulting condition is approaching for strongly
decaying sparse signals. Finally, in the noiseless setting, we prove that the
proposed conditions, in particular the bound , are the tightest
achievable guarantees based on mutual coherence