基于结构稀疏性的信号频谱估计算法研究

发布时间：2018-12-11 06:49

【摘要】：压缩感知打破传统的采样定理，利用信号的稀疏性，能够用较少的采样点数精确地恢复原始信号。对于近几年提出的结构稀疏信号受到广泛关注，其变换域的非零元素聚集分布，利用其信号分布特点能达到更好的频谱估计效果，但是往往忽略了信号在结构内部的稀疏问题，本文在上述理论的研究基础上，对结构内稀疏的信号频谱估计算法进行了深入研究。首先，本文对压缩感知理论框架及主要内容进行深入研究。包括观测矩阵、稀疏矩阵设计、信号重构算法以及压缩感知中的一些重要定理：受限等距性质和不相关定理，并且就结构稀疏信号的分布特点进行研究。其次，传统的结构稀疏优化问题将信号的结构特点作为先验知识对信号进行重构，但是没有考虑频率表示失配的问题，在充分研究信号结构特点和信号稀疏性的基础上，提出基于分块结构和冗余框架的信号估计算法，该算法将冗余框架引入group-lasso算法估计信号和频率占用频段，结合相干抑制模型和频率插值进行频谱估计。实验结果表明，由于融合了冗余框架和信号的结构分布特点，本文所提算法对频率失配的块结构信号的重构和频率估计在鲁棒性和重构精度上都优于传统的信号估计算法。最后，对于块稀疏信号，，利用信号的分块特性能降低信号采样率，但是往往忽略块内稀疏的问题。在处理随机信号时，根据复指数的旋转不变性，将冗余字典做极坐标插值映射到超球面，对整个频域进行处理，信号和频谱估计精度高，但运行时间太长。在此基础上，本文提出基于极坐标插值的块结构稀疏信号频谱估计，将信号的分块特性与极坐标插值相结合，先去除非零频块，降低计算复杂度。实验结果表明，本文所提算法可有效减少计算时间和估计误差且鲁棒性较好。
[Abstract]:Compression sensing breaks the traditional sampling theorem and can accurately recover the original signal with less sampling points by using the sparsity of the signal. For the structural sparse signal proposed in recent years, widespread attention has been paid to the non-zero element aggregation distribution in the transform domain. Using the characteristics of the signal distribution, a better spectrum estimation effect can be achieved, but the sparse problem of the signal within the structure is often ignored. Based on the above theory, the sparse signal spectrum estimation algorithm in the structure is studied in this paper. First of all, the theoretical framework and main contents of compressed perception are deeply studied in this paper. It includes observation matrix, sparse matrix design, signal reconstruction algorithm and some important theorems in compression perception: restricted equidistant property and non-correlation theorem. The distribution characteristics of structural sparse signals are also studied. Secondly, the traditional structural sparse optimization problem uses the structural characteristics of the signal as a priori knowledge to reconstruct the signal, but does not consider the problem of frequency representation mismatch, on the basis of fully studying the signal structural characteristics and signal sparsity. A signal estimation algorithm based on block structure and redundant frame is proposed. The redundant frame is introduced into the group-lasso algorithm to estimate the signal and frequency occupation band, and the coherent suppression model and frequency interpolation are combined to estimate the frequency spectrum. The experimental results show that the proposed algorithm is more robust and accurate than the traditional signal estimation algorithm for the reconstruction and frequency estimation of the block structure signals with frequency mismatch due to the combination of the redundant frame and the structural distribution of the signals. Finally, for block sparse signals, the signal sampling rate can be reduced by using the blocking characteristics of the signals, but the problem of block sparsity is often ignored. According to the rotation invariance of complex exponent, the redundant dictionaries are interpolated to hypersphere by polar coordinates. The whole frequency domain is processed. The precision of signal and spectrum estimation is high, but the running time is too long. On this basis, this paper presents the spectral estimation of block structure sparse signal based on polar interpolation, which combines the blocking characteristic of the signal with polar interpolation, and reduces the computational complexity by removing the zero frequency block first. The experimental results show that the proposed algorithm can effectively reduce the computation time and estimate error, and the robustness is good.
【学位授予单位】：燕山大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN911.23

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