基于张量对角化的多数据集信号联合盲分离

发布时间：2018-04-27 14:58

本文选题：联合盲分离 + 张量对角化　；参考：《大连理工大学》2016年硕士论文

【摘要】：现代信号处理中,在众多实际问题的驱动下,多数据集联合盲分离已成为信号处理领域新的热点。联合盲分离能够利用多数据集信号之间的统计特性,如组间相关性和组内独立性等,最终恢复出混合的源信号。而张量作为一种极具潜力的多维数据融合的工具,通过使用张量分解,(稀疏)非负矩阵／张量分解,凸优化等数学工具,也可以更好地进行盲信号的处理。若能将张量分解和联合盲分离结合起来,将大大地推动张量信号处理、联合盲分离等前沿技术在理论与方法上的发展。基于张量对角化的联合盲分离主要思想是构造具有特定结构的目标张量,进行代数拟合,辨识信号的混合机理,进行联合信号的处理,最终恢复出混合的源信号。目前基于张量分解的联合盲分离正处于起步阶段,本文主要开展了基于张量对角化的联合盲分离方法的研究,分别提出了基于Givens旋转矩阵,LU分解和连续旋转策略的三阶及四阶张量对角化算法,并将这些算法应用至实际的联合盲分离问题中,具体成果如下：(1)针对三阶正交的联合盲分离问题,提出了一种基于Givens旋转矩阵的三阶正交张量对角化算法。该算法求解一系列的Givens旋转矩阵的解析解来交替更新每一个混合矩阵。仿真实验表明,该算法与现有的算法相比具有快速的收敛性以及较高的分离精度,并通过胎儿心电图分离和语音信号分离的实验,进一步阐述了所提算法的性能。(2)针对四阶正交的联合盲分离问题,提出了一种基于Givens旋转矩阵的四阶正交张量对角化算法。通过极分解,把多个参数优化问题分解为一系列简单的特征值分解问题。仿真实验证明了该算法较优的收敛性能、分离精度,并且将其应用于解决胎儿心电信号的分离问题上。(3)针对四阶非正交的联合盲分离问题,提出了一种基于LU分解和连续旋转的四阶非正交张量对角化算法。该算法通过LU分解将复杂的整体优化问题转化成L阶段和U阶段,将因子矩阵近似地由一系列简单的初等三角矩阵或酉矩阵代替。仿真实验证明了该算法的收敛性和分离精度,并将其应用于解决胎儿心电信号的分离问题中。
[Abstract]:In modern signal processing, driven by many practical problems, multi-dataset joint blind separation has become a new hotspot in the field of signal processing. Joint blind separation can recover the mixed source signals by using the statistical characteristics of multi-dataset signals such as inter-group correlation and intra-group independence. As a potential multidimensional data fusion tool, Zhang Liang can process blind signals better by using Zhang Liang decomposition (sparse) nonnegative matrix / Zhang Liang decomposition, convex optimization and other mathematical tools. If Zhang Liang decomposition can be combined with joint blind separation, it will greatly promote the development of the theory and method of Zhang Liang signal processing and joint blind separation. The main idea of joint blind separation based on Zhang Liang's diagonalization is to construct a special structure of the target Zhang Liang, to carry out algebraic fitting, to identify the mixing mechanism of the signal, to process the combined signal, and finally to recover the mixed source signal. At present, the joint blind separation based on Zhang Liang decomposition is in its infancy. In this paper, we mainly study the joint blind separation method based on Zhang Liang diagonalization. The third and fourth order Zhang Liang diagonalization algorithms based on Givens rotation matrix LU decomposition and continuous rotation strategy are proposed, and these algorithms are applied to the practical joint blind separation problem. The main results are as follows: 1) for the third order orthogonal joint blind separation problem, a third order orthogonal Zhang Liang diagonalization algorithm based on Givens rotation matrix is proposed. The algorithm solves a series of analytical solutions of Givens rotation matrix to update each hybrid matrix alternately. The simulation results show that the proposed algorithm has fast convergence and high separation accuracy compared with the existing algorithms. The experiments of fetal electrocardiogram separation and speech signal separation are carried out. Furthermore, the performance of the proposed algorithm is discussed. (2) aiming at the joint blind separation problem of fourth-order orthogonal, a quadrature Zhang Liang diagonalization algorithm based on Givens rotation matrix is proposed. By polar decomposition, multiple parameter optimization problems are decomposed into a series of simple eigenvalue decomposition problems. The simulation results show that the proposed algorithm has better convergence performance and better separation accuracy, and is applied to solve the separation of fetal ECG signals. (3) for the fourth order non-orthogonal joint blind separation problem, the proposed algorithm is applied to the separation of fetal ECG signals. A fourth order non-orthogonal Zhang Liang diagonalization algorithm based on LU decomposition and continuous rotation is proposed. The algorithm transforms the complex global optimization problem into L and U stages by LU decomposition and replaces the factor matrix by a series of simple elementary triangular or unitary matrices. Simulation results show that the algorithm is convergent and accurate, and it is applied to the separation of fetal ECG signals.
【学位授予单位】：大连理工大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：TN911.7

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