## Recovery of exact sparse representations in the presence of bounded noise (2005)

Venue: | IEEE Trans. on I.T |

Citations: | 78 - 5 self |

### BibTeX

@ARTICLE{Fuchs05recoveryof,

author = {Jean-jacques Fuchs},

title = {Recovery of exact sparse representations in the presence of bounded noise},

journal = {IEEE Trans. on I.T},

year = {2005},

pages = {3601--3608}

}

### Years of Citing Articles

### OpenURL

### Abstract

The purpose of this contribution is to extend some recent results on sparse representations of signals in redundant bases developed in the noise-free case to the case of noisy observations. The type of questions addressed so far is: given a (n,m)-matrix with and a vector, find a sufficient condition for to have an unique sparsest representation as a linear combination of the columns of. The answer is a bound on the number of nonzero entries of say, that guaranties that is the unique and sparsest solution of with. We consider the case where satisfies the sparsity conditions requested in the noise-free case and seek conditions on, a vector of additive noise or modeling errors, under which can be recovered from in a sense to be defined. 1.