稀疏时变信号压缩感知重构算法的研究

发布时间：2018-04-10 23:22

本文选题：压缩感知 + 稀疏时变信号　；参考：《南京理工大学》2014年硕士论文

【摘要】：压缩感知是从信号稀疏表示和函数逼近理论发展形成的信号低速率采样理论。它以稀疏信号为研究对象,通过随机线性映射将稀疏信号投影到低维空间实现信号的低速采样。信号重构则通过稀疏优化算法获得。信号的稀疏性是应用压缩感知理论获取低速采样的前提。传统压缩感知理论研究的稀疏信号是非时变的。但是,在雷达、通信和导航等实际应用中,信号的稀疏性通常是随时间变化的。因此研究稀疏时变信号的压缩感知具有重要的实际意义。本文以脉冲雷达为应用背景研究稀疏时变信号压缩感知重构算法。根据脉冲雷达回波信号的时变特征,建立稀疏时变信号模型,发展基于迭代重加权的稀疏时变信号重构算法。在此基础上,以正交压缩采样系统为例,对脉冲雷达回波信号的压缩感知和动态重构问题进行研究。本文的主要工作如下： 1.简述压缩感知和信号稀疏表示的基本理论。首先简要介绍信号的稀疏表示、信号的压缩测量及信号重构问题；然后,对主要的压缩感知重构算法进行了分类总结,对其中与本文工作密切相关的迭代重加权算法进行了详细介绍；最后通过仿真实验对几种典型的稀疏信号重构算法进行了性能比较。 2.发展稀疏时变信号重构算法。本文提出将稀疏信号重构中的迭代重加权思想应用于重构稀疏时变信号,使用加权的方式将信号先验信息融入重构过程中以跟踪信号稀疏性的变化,发展了倒数加权l1范数最小化算法(RWL1)和多次倒数加权l1范数最小化算法(M-RWL1)。仿真分析了时域稀疏时变信号的重构性能,结果表明,本文提出的RWL1和M-RWL1算法可以高精度重构稀疏时变信号,从而验证了本文所提出的迭代重加权策略对稀疏时变信号重构是有效的。相比RWL1算法,M-RWL1算法由于采用了多次循环迭代的策略可获得更好的重构性能。 3.研究脉冲雷达回波信号的压缩感知重构问题。采用正交压缩采样系统获取脉冲雷达回波信号的压缩测量,将本文所提出的RWL1和M-RWL1算法用于重构脉冲雷达回波信号。仿真实验的结果表明,本文提出的稀疏时变信号重构算法可有效实现脉冲雷达回波信号的动态重构。
[Abstract]:Compression sensing is a low rate sampling theory developed from signal sparse representation and function approximation theory.The sparse signal is used as the research object and the sparse signal is projected to the low dimensional space by the random linear mapping to realize the low speed sampling of the signal.Signal reconstruction is obtained by sparse optimization algorithm.The sparsity of signal is the premise of using compression sensing theory to obtain low-speed sampling.The sparse signals studied by traditional compression sensing theory are non-time-varying.However, in radar, communication and navigation applications, the sparsity of signals usually varies with time.Therefore, it is of great practical significance to study the compressed perception of sparse time-varying signals.In this paper, the sparse time-varying signal compression perception reconstruction algorithm is studied in the background of pulse radar.According to the time-varying characteristics of pulse radar echo signal, a sparse time-varying signal model is established, and an iterative reweighted sparse time-varying signal reconstruction algorithm is developed.Taking orthogonal compression sampling system as an example, the compression sensing and dynamic reconstruction of pulse radar echo signal are studied.The main work of this paper is as follows:1.The basic theory of compressed sensing and sparse representation of signals is briefly described.Firstly, the sparse representation of signal, the compression measurement of signal and the problem of signal reconstruction are briefly introduced, and then the main algorithms of compression perception reconstruction are classified and summarized.The iterative reweighting algorithm, which is closely related to the work in this paper, is introduced in detail, and the performance of several typical sparse signal reconstruction algorithms is compared by simulation experiments.2.A sparse time-varying signal reconstruction algorithm is developed.In this paper, the idea of iterative reweighting in sparse signal reconstruction is applied to reconstruct sparse time-varying signal, and the prior information of signal is incorporated into the reconstruction process to track the change of signal sparsity.The inverse weighted l 1 norm minimization algorithm (RWL 1) and the multiple reciprocal weighted l 1 norm minimization algorithm (M RWL 1) are developed.Simulation results show that the proposed RWL1 and M-RWL1 algorithms can reconstruct sparse time-varying signals with high accuracy.It is proved that the iterative reweighting strategy proposed in this paper is effective for sparse time-varying signal reconstruction.Compared with RWL1 algorithm, M-RWL1 algorithm can achieve better reconstruction performance because of the strategy of multiple iterations.3.The problem of compression sensing reconstruction of pulse radar echo signal is studied.The compression measurement of pulse radar echo signal is obtained by orthogonal compression sampling system. The RWL1 and M-RWL1 algorithms proposed in this paper are used to reconstruct the pulse radar echo signal.The simulation results show that the sparse time-varying signal reconstruction algorithm proposed in this paper can effectively realize the dynamic reconstruction of pulse radar echo signal.
【学位授予单位】：南京理工大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN957.51

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