文档介绍：基于步移正交匹配追踪算法的图像压缩感知技术研究
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。压缩感知理论利用原始图像或信号的稀疏性先验知识,通过适当的优化算法,可以由少量的观测值或采样值对信号进行精确重建。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。
本文研究的主要内容是重构算法,它是压缩感知理论核心中的关键部分,直接决定着重构信号的质量及重构速度、应用效果。重构算法的关键在于如何从压缩感知得到的低维数据中准确地恢复出原始的高维数据。目前看来重构算法主要可以归结为三大类,即贪婪算法,凸优化算法和组合算法。三种算法各有优势,但作为基础算法,贪婪算法中的正交匹配追踪算法对后来陆续提出和改良的算法具有重要的指导意义。
本文通过对压缩感知理论及国内外现有的重建算法进行了学习之后,选择步移正交匹配追踪算法进行重点研究,主要完成工作如下:
在总结现有的各种算法及模型如最小L0范数模型,OMP算法,StOMP算法的基础之上,分别从一维信号和二维可压缩信号的角度考察StOMP算法的相对误差、匹配度及运行时间。利用matlab m语言与C语言搭建了仿真平台,对StOMP算法进行了仿真研究。此外对比了几种典型贪婪算法的性能和复杂度。
关键词:压缩感知;稀疏变换;匹配追踪;重建算法
Abstract
Compressed sensing is a novel sampling theory which is proposed by Donoho and Candès. This theory is under the condition that the signal pressible 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. For sparse pressive signal, it can be reconstructed exactly by using the appropriate reconstruction algorithms. Compressed theory breaks though the traditional Nyquist sampling theory, which es 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.
pressed 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.
The main content of this thesis is recon