基于小波模极大值点的信号稀疏表示及压缩感知重构
发布时间：2018-08-27 14:39
【摘要】：随着信息技术的飞速发展,传统的Shannon/Nyquist采样定理已不能满足日益增长的海量数据的存储、传输、处理等问题,这就需要更强大更高速的信号处理理论和算法,也需要进一步提升硬件设备的信号处理能力。近年来,Candes、Donoho和华裔数学家Tao等人提出了一种新的信息获取理论——压缩感知理论(Compressed Sensing,CS)。该理论的本质为可压缩信号(在某个基上具有稀疏描述)的少量随机线性投影就包含了该信号重构和处理的随机信息,也就是仅仅利用信号稀疏或可压缩的先验知识和少量全局线性测量就可以获得信号的精确重建。 稀疏表示和恢复算法一直是压缩感知理论的核心内容,因此,本文围绕稀疏表示和重构算法问题做了以下几方面的工作： 1简单介绍了压缩感知理论的基本框架和流程,针对压缩感知理论中信号的稀疏表示、观测矩阵的设计以及信号的重构算法等核心问题进行了详细分析,阐述了压缩感知理论的初步应用,为本文的算法研究奠定了理论基础。 2针对信号的稀疏表示问题,本文提出了基于小波模极大值搜索的信号稀疏表示方法,以及对应的信号重构算法。首先,该方法在小波变换的基础上,寻找各层小波系数的模极大值点,并根据模极大值点的传播特性对其进一步优化处理,使得信号的稀疏性得到显著提高。然后,将稀疏化的信号通过观测矩阵得到它的观测值,对观测值进行熵编码以实现数据压缩传输。解码时,采用正交匹配追踪算法得到模极大值点的估计值,最后用交替投影算法重构出原始信号。仿真结果表明,与经典压缩感知算法相比,该算法的信号重构质量有较大提高,且由于稀疏度增大,信号具有更好的可压缩性,实验表明本文算法对复杂信号效果更明显。 3针对二维信号的重构问题,本文对基于小波域树形结构的回溯正交匹配追踪算法(TBOMP)的搜索小波子树的部分进行改进,根据小波树形结构的特点,结合贪婪树逼近,提出了倒置小波子树搜索的方法,使搜索过程更加有效、简单,然后通过回溯删除的思想进一步优化搜索结果,最后将该算法应用到二维图像重构中。仿真结果表明,与原有同类压缩感知算法相比,该算法的信号重构质量大大提高。
[Abstract]:With the rapid development of information technology, the traditional Shannon/Nyquist sampling theorem can not meet the growing problems of massive data storage, transmission, processing and so on, which requires more powerful and high-speed signal processing theory and algorithm. It is also necessary to further enhance the signal processing capability of hardware devices. In recent years, Candesus Donoho and Tao et al., a Chinese mathematician, have proposed a new information acquisition theory, the theory of compressed perception (Compressed Sensing,CS). The essence of this theory is that a small number of random linear projections of compressible signals (with sparse descriptions on a basis) contain random information for the reconstruction and processing of the signals. In other words, the accurate reconstruction of the signal can be obtained by using only the prior knowledge of sparse or compressible signal and a few global linear measurements. Sparse representation and restoration algorithms have always been the core of compressed sensing theory, so, In this paper, we focus on sparse representation and reconstruction algorithms in the following aspects: 1 the basic framework and flow of compressed perception theory are briefly introduced, and the sparse representation of signals in compressed sensing theory is discussed. The design of observation matrix and the algorithm of signal reconstruction are analyzed in detail, and the preliminary application of compression sensing theory is expounded, which lays a theoretical foundation for the research of the algorithm in this paper. In this paper, a signal sparse representation method based on wavelet modulus maximum search and corresponding signal reconstruction algorithm are proposed. Firstly, on the basis of wavelet transform, this method finds the modulus maximum points of wavelet coefficients in each layer, and optimizes the processing according to the propagation characteristics of the modulus maximum points, so that the sparsity of signals is improved significantly. Then, the sparse signal is obtained by the observation matrix, and the observed value is encoded by entropy to realize the data compression and transmission. In decoding, the orthogonal matching tracking algorithm is used to obtain the estimation of the modulus maximum, and the original signal is reconstructed by alternating projection algorithm. The simulation results show that compared with the classical compression sensing algorithm, the signal reconstruction quality of this algorithm is improved greatly, and the signal has better compressibility because of the increase of sparsity. Experiments show that the algorithm is more effective for complex signals. 3 aiming at the reconstruction of two-dimensional signals, this paper improves the search of wavelet subtree based on (TBOMP), a backtracking orthogonal matching algorithm based on the tree structure in wavelet domain. According to the characteristics of wavelet tree structure and greedy tree approximation, an inverted wavelet subtree search method is proposed, which makes the search process more efficient and simple. Then the search results are optimized by the idea of backtracking deletion. Finally, the algorithm is applied to 2D image reconstruction. The simulation results show that the signal reconstruction quality of this algorithm is greatly improved compared with the original similar compression sensing algorithm.
【学位授予单位】：北京交通大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN911.7
本文编号：2207588
[Abstract]:With the rapid development of information technology, the traditional Shannon/Nyquist sampling theorem can not meet the growing problems of massive data storage, transmission, processing and so on, which requires more powerful and high-speed signal processing theory and algorithm. It is also necessary to further enhance the signal processing capability of hardware devices. In recent years, Candesus Donoho and Tao et al., a Chinese mathematician, have proposed a new information acquisition theory, the theory of compressed perception (Compressed Sensing,CS). The essence of this theory is that a small number of random linear projections of compressible signals (with sparse descriptions on a basis) contain random information for the reconstruction and processing of the signals. In other words, the accurate reconstruction of the signal can be obtained by using only the prior knowledge of sparse or compressible signal and a few global linear measurements. Sparse representation and restoration algorithms have always been the core of compressed sensing theory, so, In this paper, we focus on sparse representation and reconstruction algorithms in the following aspects: 1 the basic framework and flow of compressed perception theory are briefly introduced, and the sparse representation of signals in compressed sensing theory is discussed. The design of observation matrix and the algorithm of signal reconstruction are analyzed in detail, and the preliminary application of compression sensing theory is expounded, which lays a theoretical foundation for the research of the algorithm in this paper. In this paper, a signal sparse representation method based on wavelet modulus maximum search and corresponding signal reconstruction algorithm are proposed. Firstly, on the basis of wavelet transform, this method finds the modulus maximum points of wavelet coefficients in each layer, and optimizes the processing according to the propagation characteristics of the modulus maximum points, so that the sparsity of signals is improved significantly. Then, the sparse signal is obtained by the observation matrix, and the observed value is encoded by entropy to realize the data compression and transmission. In decoding, the orthogonal matching tracking algorithm is used to obtain the estimation of the modulus maximum, and the original signal is reconstructed by alternating projection algorithm. The simulation results show that compared with the classical compression sensing algorithm, the signal reconstruction quality of this algorithm is improved greatly, and the signal has better compressibility because of the increase of sparsity. Experiments show that the algorithm is more effective for complex signals. 3 aiming at the reconstruction of two-dimensional signals, this paper improves the search of wavelet subtree based on (TBOMP), a backtracking orthogonal matching algorithm based on the tree structure in wavelet domain. According to the characteristics of wavelet tree structure and greedy tree approximation, an inverted wavelet subtree search method is proposed, which makes the search process more efficient and simple. Then the search results are optimized by the idea of backtracking deletion. Finally, the algorithm is applied to 2D image reconstruction. The simulation results show that the signal reconstruction quality of this algorithm is greatly improved compared with the original similar compression sensing algorithm.
【学位授予单位】：北京交通大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN911.7
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