SCIENCE@home

A new bound on the block restricted isometry constant in compressed sensing

Yi Gao,Mingde Ma

Published 2017 in Journal of Inequalities and Applications

ABSTRACT

This paper focuses on the sufficient condition of block sparse recovery with the l2/l1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$l_{2}/l_{1}$\end{document}-minimization. We show that if the measurement matrix satisfies the block restricted isometry property with δ2s|I<0.6246\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\delta_{2s|\mathcal{I}}< 0.6246$\end{document}, then every block s-sparse signal can be exactly recovered via the l2/l1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$l_{2}/l_{1}$\end{document}-minimization approach in the noiseless case and is stably recovered in the noisy measurement case. The result improves the bound on the block restricted isometry constant δ2s|I\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\delta_{2s|\mathcal {I}}$\end{document} of Lin and Li (Acta Math. Sin. Engl. Ser. 29(7):1401-1412, 2013).

PUBLICATION RECORD

CITATION MAP

EXTRACTION MAP

CLAIMS

  • No claims are published for this paper.

CONCEPTS

  • No concepts are published for this paper.

REFERENCES

Showing 1-33 of 33 references · Page 1 of 1

CITED BY

Showing 1-16 of 16 citing papers · Page 1 of 1