English

Robust analysis $\ell_1$-recovery from Gaussian measurements and total variation minimization

Information Theory 2015-10-28 v2 math.IT

Abstract

Analysis 1\ell_1-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}
}