Recovery of exact sparse representations in the presence of bounded noise

摘要: The purpose of this contribution is to extend some recent results on sparse representations signals in redundant bases developed the noise-free case noisy observations. type question addressed so far as follows: given an (n,m)-matrix A with m>n and a vector b=Axo, i.e., admitting representation xo, find sufficient condition for b have unique sparsest representation. answer bound number nonzero entries xo. We consider b=Axo+e where xo satisfies sparsity conditions requested e additive noise or modeling errors, seek under which can be recovered from sense defined. we obtain relate energy signal level well parameter quadratic program use recover unknown When signal-to-noise ratio large enough, all components are still present when deleted; otherwise, smallest themselves erased quite rational predictable way