基于压缩感知的正交匹配算法图像重建_毕业设计论文西安文理学院.docVIP

基于压缩感知的正交匹配算法图像重建 摘要：压缩感知理论是由Donoho和Candes提出的一种充分利用信号稀疏性的全新的信号采样理论。该理论表明，用远低于Nyquist采样定理要求的频率对信号进行采样也能实现信号的精确重构。该理论突破了传统的以Nyquist定理为基准的信号处理方法，实现了在获取数据的同时对其进行适当的压缩，克服了采样数据量大，采样时间长及数据存储空间浪费严重的问题，因此进一步降低了信号处理的时间和器件成本。 压缩感知理论有三个核心方面：（1）稀疏变换，即对一个非稀疏的信号，找到一个合适的正交基使该信号在它上可以稀疏表示；（2）测量矩阵，与变换基不相干且平稳的矩阵；（3）重构算法，利用数学算法完成对信号的精确重构，该过程可看为求解一个优化问题。 本文介绍了主要介绍了压缩感知原理和目前最为成熟的压缩感知重建算法——正交匹配追踪算法，通过MATLAB平台设计实现了基本的正交匹配追踪算法，对一维、二维信号进行了重建仿真。 关键词Based On Compressed Sensing Of Orthogonal Matching Algorithm Image Recovery Abstract：Compressed sensing is a novel sampling theory which is proposed by Donoho and Candès. This theory is under the condition that the signal is compressible or sparse. In this case, using far less than the required sampling frequency of the Nyquist theory to sample the signal is able to accurately reconstruct the signal.Compressed theory breaks though the traditional Nyquist sampling theory, which overcomes a lot of problems such as a great number of sampling data, time wasting, data storage space wasting and so on. As a result, it reduces signal processing cost and device cost. The compressed theory has three key sides: (1) Sparse transformation, for a non- sparse signal, we need to find a proper orthogonal basis on which the signal has a sparse representation; (2) Observation matrix, it is irrelevant with the orthogonal basis; (3) reconstruction algorithms, using a reconstruction algorithm to ensure the accuracy of the signal reconstruction, the whole process can be considered as the solve to a optimization problem. This paper introduces CS and most mature compression perception algorithm at present-Orthogonal matching algorithm. Through the MATLAB design realize basic orthogonal matching algorithms, Through the MATLAB design realize basic orthogonal matching algorithm of one-dimensional, two-dimensional signal processing simulation. Key words：Compressed sensing; Sparse transform; Orthogonal matching; Image recovery. 目 录 第一章 绪论 2 1.1选题的背景及意义 2 1.2本课题在国内外的发展现状 2 1.3