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

Junhan Kim, Byonghyo Shim

Research output: Contribution to journalArticlepeer-review

6 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

Keywords

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

ASJC Scopus subject areas

  • Computer Science(all)
  • Materials Science(all)
  • Engineering(all)

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