### 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 |
---|---|

Article number | 8674762 |

Pages (from-to) | 46822-46830 |

Number of pages | 9 |

Journal | IEEE Access |

Volume | 7 |

DOIs | |

Publication status | Published - 2019 Jan 1 |

### Fingerprint

### 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

*IEEE Access*,

*7*, 46822-46830. [8674762]. https://doi.org/10.1109/ACCESS.2019.2907303

**A Near-Optimal Restricted Isometry Condition of Multiple Orthogonal Least Squares.** / Kim, Junhan; Shim, Byonghyo.

Research output: Contribution to journal › Article

*IEEE Access*, vol. 7, 8674762, pp. 46822-46830. https://doi.org/10.1109/ACCESS.2019.2907303

}

TY - JOUR

T1 - A Near-Optimal Restricted Isometry Condition of Multiple Orthogonal Least Squares

AU - Kim, Junhan

AU - Shim, Byonghyo

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - multiple OLS (MOLS)

KW - orthogonal least squares (OLS)

KW - restricted isometry property (RIP)

KW - Sparse signal recovery

UR - http://www.scopus.com/inward/record.url?scp=85065160423&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85065160423&partnerID=8YFLogxK

U2 - 10.1109/ACCESS.2019.2907303

DO - 10.1109/ACCESS.2019.2907303

M3 - Article

VL - 7

SP - 46822

EP - 46830

JO - IEEE Access

JF - IEEE Access

SN - 2169-3536

M1 - 8674762

ER -