西安电子科技大学学报 ›› 2024, Vol. 51 ›› Issue (4): 39-50.doi: 10.19665/j.issn1001-2400.20231204

• 信息与通信工程 • 上一篇    下一篇

一种自适应加速的多路径匹配追踪重建算法

逯彦1(), 廖桂生2(), 王小鹏1()   

  1. 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
  • 收稿日期:2023-07-23 出版日期:2024-08-20 发布日期:2024-01-17
  • 作者简介:逯彦(1989—),男,讲师,E-mail:tyccly123@126.com
    廖桂生(1963—),男,教授,E-mail:gsliao@xidian.edu.cn
    王小鹏(1968—),男,教授,E-mail:wangxiaopeng@mail.lzjtu.cn
  • 基金资助:
    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)

Algorithm for the reconstruction of adaptive acceleration multi-path matching pursuit

LU Yan1(), LIAO Guisheng2(), WANG Xiaopeng1()   

  1. 1. School of Electronic and Information Engineering,Lanzhou Jiaotong University,Lanzhou 730070,China
    2. National Key Laboratory of Radar Signal Processing,Xidian University,Xi’an 710071,China
  • Received:2023-07-23 Online:2024-08-20 Published:2024-01-17

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。

关键词: 压缩感知, 多路径匹配追踪, 相干性, 有限等距性

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.

Key words: compressed sensing, multi-path matching pursuit, coherence, restricted isometry property

中图分类号: 

  • TP391