On recoverability properties of fixed measurement matrices
Information Theory
2014-12-25 v1 math.IT
Abstract
The purpose of this paper is to extend a result by Donoho and Huo, Elad and Bruckstein, Gribnoval and Nielsen on sparse representations of signals in dictionaries to general matrices. We consider a general fixed measurement matrix, not necessarily a dictionary, and derive sufficient condition for having unique sparse representation of signals in this matrix. Currently, to the best of our knowledge, no such method exists. In particular, if matrix is a dictionary, our method is at least as good as the method proposed by Gribnoval and Nielsen.
Cite
@article{arxiv.1412.7748,
title = {On recoverability properties of fixed measurement matrices},
author = {Anatoly Eydelzon},
journal= {arXiv preprint arXiv:1412.7748},
year = {2014}
}