一种自适应加速的多路径匹配追踪重建算法

逯彦; 廖桂生; 王小鹏

doi:10.19665/j.issn1001-2400.20231204

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一种自适应加速的多路径匹配追踪重建算法

信息与通信工程 | 更新时间：2024-11-13

- 一种自适应加速的多路径匹配追踪重建算法
- Algorithm for the reconstruction of adaptive acceleration multi-path matching pursuit
- 西安电子科技大学学报 2024年51卷第4期页码：39-50
- 作者机构：
  
  1. 兰州交通大学电子与信息工程学院,甘肃兰州 730070
  2. 西安电子科技大学雷达信号处理全国重点实验室,陕西西安 710071
- 作者简介：
  
  [ "逯彦(1989—),男,讲师,E-mail:[email protected]" ]
  [ "廖桂生(1963—),男,教授,E-mail:[email protected]" ]
  [ "王小鹏(1968—),男,教授,E-mail:[email protected]" ]
- 基金信息：
  
  国家自然科学基金(61761027);甘肃省青年科技基金(22JR5RA381);甘肃省高校产业支撑计划项目(2023CYZC-40)
- DOI：10.19665/j.issn1001-2400.20231204
  中图分类号： TP391
- 纸质出版日期：2024-08-20，
  
  网络出版日期：2024-01-17，
  
  收稿日期：2023-07-23，
- 稿件说明：
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逯彦, 廖桂生, 王小鹏. 一种自适应加速的多路径匹配追踪重建算法[J]. 西安电子科技大学学报, 2024,51(4):39-50.

Yan LU, Guisheng LIAO, Xiaopeng WANG. Algorithm for the reconstruction of adaptive acceleration multi-path matching pursuit. [J]. Journal of Xidian University, 2024,51(4):39-50.
逯彦, 廖桂生, 王小鹏. 一种自适应加速的多路径匹配追踪重建算法[J]. 西安电子科技大学学报, 2024,51(4):39-50. DOI： 10.19665/j.issn1001-2400.20231204.

Yan LU, Guisheng LIAO, Xiaopeng WANG. Algorithm for the reconstruction of adaptive acceleration multi-path matching pursuit. [J]. Journal of Xidian University, 2024,51(4):39-50. DOI： 10.19665/j.issn1001-2400.20231204.

摘要

在压缩感知重建算法中

多路径匹配追踪算法能够通过搜索多个路径提升获得全局最优解的可能性

但产生的大量冗余路径会造成严重的性能损耗。针对此问题

提出了一种基于自适应加速的多路径匹配追踪重建算法。首先

该算法在路径分解时

通过设置阈值门限控制生成的子枝点数量

优化了原算法平均分配路径数的策略

使相干性强的父枝点可以遍历更多的子枝点

限制相干性小的原子被分配到新的路径中;其次

利用首个路径产生的重建残差

设计了新的修剪准则对候选路径进行二次筛选

进一步减少冗余路径的生成

降低了计算支出;最后

在理论上推导了所提算法在理想状态下准确重建信号的有限等距性条件

给出了所提算法在有噪条件下准确重建信号的信噪比界限。仿真结果表明

在一维和二维信号的重建实验中

所提算法在保证较高的重建精度的前提下

与多路径匹配追踪算法相比

有效提升了重建效率。

Abstract

In compressive sensing reconstruction algorithms

the multi-path matching pursuit algorithm improves the possibility of obtaining the global optimal solution by searching multiple paths

but a large number of redundant paths will cause a serious drop in performance.To solve this problem

a multi-path matching pursuit reconstruction algorithm based on adaptive acceleration is proposed.First

the number of generated child branches is controlled by setting the threshold

optimizing the strategy of the original algorithm in allocating the number of paths evenly

so that the parent branches with a strong coherence traverse more child branches and atoms with a low coherence are restricted from being assigned to new paths.Second

by using the reconstruction residuals generated by the first path

a new pruning criterion is designed to perform secondary screening on candidate paths

thus reducing computational expenses.Finally

under an ideal state

the proposed algorithm derives the restricted isometry property condition to accurately reconstruct the signal

and presents the signal-to-noise ratio limit for the accurate reconstruction of the signal in the presence of noise interference.Simulation results show that in the reconstruction experiments for one-dimensional and two-dimensional signals

the proposed algorithm effectively improves the reconstruction efficiency compared to the multi-path matching pursuit algorithm

while ensuring a high reconstruction accuracy.

关键词

压缩感知多路径匹配追踪相干性有限等距性

Keywords

compressed sensingmulti-path matching pursuitcoherencerestricted isometry property

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