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

Junhan Kim, Byonghyo Shim

Research output: Contribution to journalArticle

### 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 language English 8674762 46822-46830 9 IEEE Access 7 https://doi.org/10.1109/ACCESS.2019.2907303 Published - 2019 Jan 1

Sampling
Recovery

### Keywords

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

### ASJC Scopus subject areas

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

### Cite this

In: IEEE Access, Vol. 7, 8674762, 01.01.2019, p. 46822-46830.

Research output: Contribution to journalArticle

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