【作者】 文首先；

【导师】 李晓辉；

【作者基本信息】 安徽大学 ， 通信与信息系统， 2013， 硕士

【摘要】 压缩感知理论是建立在概率统计理论、矩阵分析理论、泛函分析以及拓扑学等基础学科之上的信号处理理论框架。对于稀疏信号或者可稀疏化表示的信号,可将信号采样与信号压缩过程合二为一,信号重构过程则采用非线性算法。该理论框架为许多实际信号处理问题提供了更加良好的解决方案。相比较传统方法而言,压缩感知理论突破了奈奎斯特采样定律的要求,可通过少量采样点完成信号的重构,可降低硬件设备的复杂度以及避免采样、传输和存储过程因处理冗余信息而浪费资源。目前,虽然压缩感知理论方面的研究已经取得了一些重要的成果,但是还停留在初步探索阶段,对于压缩感知理论的三个主要部分：信号的稀疏变换、观测矩阵的设设计和信号重构算法仍然需要我们不断的探索研究。作为压缩感知理论的核心部分,信号重构过程直接影响到了信号重构的速度、质量等。本文通过对压缩感知理论研究现状的分析,以及详细介绍压缩感知理论基本框架的基础上,围绕了匹配追踪算法所存在的问题展开研究,其主要工作如下：本文首先介绍了压缩感知研究的目的和意义以及国内外相关领域的研究现状,对压缩感知理论的基本框架进行了详细的介绍,重点分析了压缩感知理论中信号的稀疏表示、观测矩阵的设计和信号重构。然后对信号重构进行了详细的分析针对其中比较具有代表性的基追踪算法、匹配追踪算法、正交匹配追踪算法以及分段正交匹配追踪算法的基本原理、重构思想以及主要步骤的算法流程图进行分析对比。分别对一维时域脉冲信号和二维图像进行了重构仿真,简要分析不同算法各自的优缺点。最后通过引入Dice系数作为新的原子匹配准则,将其应用到OMP算法与StOMP算法中,得到新的DOMP算法与DStOMP算法。从算法的有效性、信号重构成功率、信号重构误差与信号重构时间等方面做仿真对比,说明DOMP算法的实用性。同时把DOMP算法与DStOMP算法应用到二维图像重构中,通过对不同采样率下重构图像的时间和重构相对误差对比,分析改进算法的优缺点。更多还原

【Abstract】 Compression sensing theory is a signal processing theory framework, which is based on basic subject such as probability statistics theory, matrix analysis theory, functional analysis and topology. For sparse signal or signal which can be sparse represented, signal sampling and signal compression process can be combined into one process, and then the signal reconstruction process is a nonlinear algorithm. The theoretical framework provides a better solution for many practical problems in signal processing. Compared to traditional methods, compressed sensing theory broke through the requirement of Nyquist sampling theorem, it can finish signal processing and reconstruction process by getting a small amount of sample point, so it can reduce the complexity of hardware devices and avoid waste of resources when sampling, transporting and storaging for dealing with redundant redundant information.At present, although the study of compressed sensing theory has made some important achievements, but the study is still stay at preliminary exploration phase, for the three main parts of compressed sensing theory:signal sparse transformation, the design of the observation matrix and the signal reconstruction algorithms, we need still keeping research. As a core part of the compressed sensing theory, signal reconstruction process directly affects the signal reconstruction speed, quality, etc. In this thesis, we analyse the research status of compression sensing theory, introduce compression perception theory framework detailed, and spread the study which revolves around the problem of matching pursuit algorithm research. The main work is as follows:Firstly, we introduce the purpose and significance of compression sensing research and the related research at home and abroad, at the same time, introduce compression perception theory framework detailed, focous on analyzing the details of signal sparse representation, the design of the observation matrix and the signal reconstruction, which are the three main aspects of compression sensing theory.And then analyze the signal reconstruction in detail, for based tracking algorithm, the matching pursuit algorithm, orthogonal matching pursuit algorithm and block orthogonal matching pursuit algorithm, we analyze and compare their basic principle, reconstruct ideas and the main steps of the algorithm flow chart. We take a reconstructed simulation for one dimensional time-domain pulse signal and the2dimensional image, and then analyze the advantages and disadvantages of different algorithms respectively.At last, we introduce Dice coefficient as a new atom matching criteria, apply it to the OMP algorithm, and then we propose a new DOMP algorithm. For the DOMP algorithm, we give a simulation and analysis from the effectiveness and success rate of reconstructing signal, signal reconstruction error and signal reconstruction time, results illustrates the usefulness of DOMP algorithm. The DOMP algorithm and the DStOMP algorithm is applied to the two-dimensional image reconstruction by the relative error for different sampling rates the time and reconstruction of the reconstructed image contrast, analysis of the advantages and disadvantages of the improved algorithm.更多还原