【作者】 李维明；

【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】 传统的信号处理技术遵循奈奎斯特采样定律,信号的采样频率必须大于信号最高频率的2倍才能精确地恢复原始信号。因此,传统的信号处理技术已经不能满足日益增长的信号需求。近年来,一种新的信号处理技术被相关学者提出来,即压缩感知技术。该技术与传统的信号处理技术相比突显出巨大的优势,压缩感知技术将数据的采集和压缩合二为一,突破了奈奎斯特定理的束缚,并能精确地恢复信号。压缩感知理论一经提出,就受到了人们的广泛关注,成为信号处理领域研究的热点话题。该理论具有巨大的应用前景,无论在理论研究与实际应用中都有重要的意义。本文首先介绍了压缩感知理论的背景和研究意义,以及简单介绍了目前国内外的研究现状。然后介绍了压缩感知理论的整体框架,阐述了感知过程的三个步骤：信号的稀疏表示、观测矩阵的设计以及信号的重构算法。在信号的稀疏表示部分,介绍了信号稀疏化的基本原理；对于观测矩阵的设计,首先分析了观测矩阵的选取原则,然后给出几种常用的观测矩阵。本文主要研究的是信号的重构算法,针对几种主要的信号重构算法,重点介绍了正交匹配追踪算法及其改进算法。对几种算法进行了MATLAB仿真比较并进行了分析。基于经典的正交匹配追踪算法,其中在信号重构部分运用到最小二乘法,但是最小二乘法计算过程中矩阵的计算复杂度比较高,并且每次迭代中都要运用到最小二乘法。针对这点,对最小二乘法的原理进行了介绍,并列举了几种常用的矩阵分解方法,QR分解、cholesky分解以及奇异值分解比较适用于最小二乘法。在此基础上,将正交匹配追踪算法中的矩阵进行QR分解,推导出简化的结果。对改进算法进行仿真并进行结果分析,证实改进算法相比原算法在运算时间上有所缩短。更多还原

【Abstract】 Traditional signal processing technology follows the law of Nyquist sampling signals, that the sampling frequency must be greater than two times of the highest frequency that the signal can be accurately restore. Therefore, the traditional signal processing technology have been formed by contradiction in growing demand of signal. In recent years, a new signal processing technology was proposed by some related scholars, which is the Compressed Sensing technology. The technology demonstrated a huge advantage when it was compared with the traditional signal processing technology, which combined collection and compression of signal. It had broken the shackles of the law of Nyquist and the signal can be restored accurately. When the theory of compressed Sensing technology was put forwarded, compressed sensing theory has been received widespread attention by people, and has become a hot topic in the field of signal processing research. The theory has great application prospects, which has important significance both in filed of research theory and practical application.This thesis firstly introduces the background and the research significance of compressed sensing theory, and the research status at home and abroad is introduced simply. Then this thesis introduces the overall framework of compressed sensing theory, and expounds the three steps of the process of perception:sparse representation of signal, the design of the observation matrix and the signal reconstruction algorithm. In the part of sparse representation of signal, this thesis introduces the basic principle of signal sparse; To the design of the observation matrix, the selecting principle of the observation matrix is firstly analyzed, then several observation matrix are given. This thesis mainly studies the signal reconstruction algorithm, aiming at several main signal reconstruction algorithm, that the orthogonal matching pursuit algorithm and its improved algorithm are mainly introduced. Several algorithms for the MATLAB simulation are compared and analyzed. Based on the classical orthogonal matching pursuit algorithm, which the least squares method was used in part of signal reconstruction, but the complexity is higher in the process of matrix calculation with least squares calculation, and least squares is applied to each iteration. In the light of this, the principle of least square method is introduced, and several common methods of the matrix decomposition are listed, such as the QR decomposition, the cholesky decomposition and singular value decomposition are suitably applied to least squares. On this basis, the matrix QR decomposition is used in the orthogonal matching pursuit algorithm, and deduces the simplified results. Simulate the improved algorithm and analysis of the simulation results. It is confirmed that running time of the improved algorithm is shorter than the original algorithm.更多还原