A Near-Optimal Restricted Isometry Condition of Multiple Orthogonal Least Squares

Junhan Kim, Byonghyo Shim

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

In this paper, we analyze the performance guarantee of multiple orthogonal least squares (MOLS) in recovering sparse signals. Specifically, we show that the MOLS algorithm ensures the accurate recovery of any K -sparse signal, provided that a sampling matrix satisfies the restricted isometry property (RIP) with \begin{equation∗} \delta -{LK-L+2} < \frac {\sqrt {L}}{\sqrt {K+2L-1}}\end{equation∗} where L is the number of indices chosen in each iteration. In particular, if L=1 , our result indicates that the conventional OLS algorithm exactly reconstructs any K -sparse vector under \delta -{K+1} < \frac {1}{\sqrt {K+1}} , which is consistent with the best existing result for OLS.

Original languageEnglish
Article number8674762
Pages (from-to)46822-46830
Number of pages9
JournalIEEE Access
Volume7
DOIs
Publication statusPublished - 2019

Bibliographical note

Funding Information:
This work was supported in part by the National Research Foundation of Korea (NRFK) grant funded by the Korean Government (MSIP) (2016R1A2B3015576) and in part by the Framework of International Cooperation Program managed by NRFK (2016K1A3A1A20006019).

Publisher Copyright:
© 2013 IEEE.

Keywords

  • Sparse signal recovery
  • multiple OLS (MOLS)
  • orthogonal least squares (OLS)
  • restricted isometry property (RIP)

ASJC Scopus subject areas

  • General Computer Science
  • General Materials Science
  • General Engineering

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