A NEW SUFFICIENT CONDITION FOR SPARSE RECOVERY WITH MULTIPLE ORTHOGONAL LEAST SQUARES

doi:10.1007/s10473-022-0308-4

数学物理学报 ›› 2022, Vol. 42 ›› Issue (3): 941-956.doi: 10.1007/s10473-022-0308-4

A NEW SUFFICIENT CONDITION FOR SPARSE RECOVERY WITH MULTIPLE ORTHOGONAL LEAST SQUARES

李海锋, 张静

Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control, College of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, China

收稿日期:2020-09-02 修回日期:2021-05-28 出版日期:2022-06-26 发布日期:2022-06-24
通讯作者: Haifeng Li,E-mail:lihaifengxx@126.com E-mail:lihaifengxx@126.com
基金资助:
This work was partially supported by the National Natural Science Foundation of China (61907014, 11871248, 11701410, 61901160), Youth Science Foundation of Henan Normal University (2019QK03).

A NEW SUFFICIENT CONDITION FOR SPARSE RECOVERY WITH MULTIPLE ORTHOGONAL LEAST SQUARES

Haifeng LI, Jing ZHANG

Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control, College of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, China

Received:2020-09-02 Revised:2021-05-28 Online:2022-06-26 Published:2022-06-24
Contact: Haifeng Li,E-mail:lihaifengxx@126.com E-mail:lihaifengxx@126.com
Supported by:
This work was partially supported by the National Natural Science Foundation of China (61907014, 11871248, 11701410, 61901160), Youth Science Foundation of Henan Normal University (2019QK03).

摘要/Abstract

摘要： A greedy algorithm used for the recovery of sparse signals, multiple orthogonal least squares (MOLS) have recently attracted quite a big of attention. In this paper, we consider the number of iterations required for the MOLS algorithm for recovery of a $K$-sparse signal $\mathbf{x}\in\mathbb{R}^n$. We show that MOLS provides stable reconstruction of all $K$-sparse signals $\mathbf{x}$ from $\mathbf{y}=\mathbf{A}\mathbf{x}+\mathbf{w}$ in $\lceil\frac{6K}{M}\rceil$ iterations when the matrix $\mathbf{A}$ satisfies the restricted isometry property (RIP) with isometry constant $\delta_{7K}\leq0.094$. Compared with the existing results, our sufficient condition is not related to the sparsity level $K$.

关键词: Sparse signal recovery, multiple orthogonal least squares (MOLS), sufficient condition, restricted isometry property (RIP)

Abstract: A greedy algorithm used for the recovery of sparse signals, multiple orthogonal least squares (MOLS) have recently attracted quite a big of attention. In this paper, we consider the number of iterations required for the MOLS algorithm for recovery of a $K$-sparse signal $\mathbf{x}\in\mathbb{R}^n$. We show that MOLS provides stable reconstruction of all $K$-sparse signals $\mathbf{x}$ from $\mathbf{y}=\mathbf{A}\mathbf{x}+\mathbf{w}$ in $\lceil\frac{6K}{M}\rceil$ iterations when the matrix $\mathbf{A}$ satisfies the restricted isometry property (RIP) with isometry constant $\delta_{7K}\leq0.094$. Compared with the existing results, our sufficient condition is not related to the sparsity level $K$.

Key words: Sparse signal recovery, multiple orthogonal least squares (MOLS), sufficient condition, restricted isometry property (RIP)

中图分类号:

94A12

李海锋, 张静. A NEW SUFFICIENT CONDITION FOR SPARSE RECOVERY WITH MULTIPLE ORTHOGONAL LEAST SQUARES[J]. 数学物理学报, 2022, 42(3): 941-956.

Haifeng LI, Jing ZHANG. A NEW SUFFICIENT CONDITION FOR SPARSE RECOVERY WITH MULTIPLE ORTHOGONAL LEAST SQUARES[J]. Acta mathematica scientia,Series A, 2022, 42(3): 941-956.

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A NEW SUFFICIENT CONDITION FOR SPARSE RECOVERY WITH MULTIPLE ORTHOGONAL LEAST SQUARES

A NEW SUFFICIENT CONDITION FOR SPARSE RECOVERY WITH MULTIPLE ORTHOGONAL LEAST SQUARES

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