【作者】 毕林林；

【导师】 王学东；

【作者基本信息】 哈尔滨工业大学 ， 信息与通信工程， 2011， 硕士

【摘要】 压缩传感是一种新型的数字信号处理方法。它最大的突破在于实现了当采样点数少于奈奎斯特采样点数时也能够精确的重构出原始信号。压缩传感理论合并了采样和压缩的过程,降低了信号处理的复杂度,使其在许多领域得到了大量应用。信号的重构是压缩传感中必不可少的一部分。本文主要对压缩传感中的信号重构算法进行了深入的研究。首先,本文分析了压缩传感的基本原理,包括稀疏信号的构建、测量矩阵生成与性质以及重构算法的基本思想。在分析了压缩传感基本思想的基础之上,研究了现阶段主要存在的重构算法。并且分析了扩展图的存在性及其本身所具有特殊性质。其次,本文对最小l1范数重构算法和正交匹配追踪追踪重构算法(OMP)做了是深入研究。分析了两种算法的实现方法,研究了最小l1范数算法的求解过程,并分别给出了两种算法的仿真实现流程图。然后,本文完成了对两种算法性能的分析,在输入信号不同的条件下,分别研究了算法的重构精度与信号稀疏水平、测量矩阵个数等参数之间的关系。接着对算法的重构精度、实现复杂度和应用条件进行了分析和比较。最后,本文研究了基于扩展图理论的信号重构算法,分别设计了用扩展图算法重构稀疏信号和近似稀疏信号的仿真流程。由于精确构建扩展图是一个较难解决的问题,本文设计利用随机产生的规则的二分图作为算法中所需要的扩展图。在输入不同信号的情况下,分析了扩展图算法的可行性与算法自身的特性。最后对三种算法的重构精度和重构时间进行分析和比较,找出算法的各自优越性。更多还原

【Abstract】 Compressive sensing is a new type of digital signal processing method. The novel objective of compressive sengsing is to reconstruct a signal accurately and efficiently from far fewer sampling points got by Nyquist Sampling Theorem.Compressive sensing theory combines the process of sampling and compression to reduce the complexity of signal processing, which is widely used in many fields. Signal reconstruction is an essential part of the compressed sensing. This paper focuses on the algorithms of signal reconstruction.Firstly, the basic principle of compressive sensing, including the costruction of sparse signals, the measurement matrix and the basic idea of recongstruction algorithms is analyzed. Based on the theory of compressive sensing, the main reconstruction algotithms are summed up. Special charaters and the existence of expander graphs are discussed.Secondly, minimum l1 -norm reconstruction algorithm and Orthogonal Matching Pursuit (OMP) reconstruction algorithm are deeply studied in this paper. The realizable schemes of two methods are ananlyzed, and the solving process of minimum l1 -norm algorithm is researched. Then the simulation flow charts of two algorithms are given. We analyze the performance of minimum l1 -norm algorithm and OMP algorithm by the simulation results, respectively study the relationship amony reconstruction accuracy of the algorith、sparsity level of signals and the number of measurement entries with different input signals.Finally, the signal reconstruction algorithm using expander graph is studied. We designed the simulation system and flow of reconstruction algorithms using expander graph for sparse signal and approximate sparse signal. Explicit constructions of the considered expander graphs are very difficult. According to the theorems, we randomly generate a regular bipartite graph with a uniform distribution as the expander graph for simulation. We ananlyze the feasibility and characters of the recovery algorithm using expander graph under different input singals. Finally, we compare the accuracy of reconstruction and the recovery time of three algorithms, and analyze the respective advantages of algorithms.更多还原