Robust analysis $\ell_1$-recovery from Gaussian measurements and total variation minimization
Information Theory
2015-10-28 v2 math.IT
Abstract
Analysis -recovery refers to a technique of recovering a signal that is sparse in some transform domain from incomplete corrupted measurements. This includes total variation minimization as an important special case when the transform domain is generated by a difference operator. In the present paper we provide a bound on the number of Gaussian measurements required for successful recovery for total variation and for the case that the analysis operator is a frame. The bounds are particularly suitable when the sparsity of the analysis representation of the signal is not very small.
Keywords
Cite
@article{arxiv.1407.7402,
title = {Robust analysis $\ell_1$-recovery from Gaussian measurements and total variation minimization},
author = {Maryia Kabanava and Holger Rauhut and Hui Zhang},
journal= {arXiv preprint arXiv:1407.7402},
year = {2015}
}