基于自然梯度的盲源分离算法中非线性函数的研究

发布时间：2018-04-11 17:07

本文选题：盲源分离 + 自然梯度算法　；参考：《东北大学》2014年硕士论文

【摘要】：盲源分离是在不知源信号和传输通道先验信息的情况下,仅由观测到的混合信号恢复出源信号的过程。自然梯度算法作为盲源分离的核心算法之一,受到越来越多的关注。同时,由于自然梯度算法计算量低、收敛速度快、分离效果好等优点,凸显出其良好的应用前景,并在语音信号处理、图像处理、无线通信领域等领域有了广泛的应用。论文介绍了盲源分离的背景和基本理论；通过介绍盲源分离的三种基本模型,讨论了盲源分离的可解性；从优化算法的角度出发,介绍了几种常用的代价函数,并引出了经典的盲源分离算法——自然梯度算法,讨论了非线性函数对其的影响；同时给出了非线性函数的构造方法及常用的非线性函数。针对瞬时线性混叠情况下自然梯度盲源分离算法中存在的一些问题,尤其是对不同源信号,分离矩阵中非线性函数的选择问题进行研究,提出了两种改进的非线性函数。一种是针对传统自然梯度算法中,对所有源信号都采用同一非线性函数所引起的分离误差较大问题,引入了皮尔逊系统,将皮尔逊系统与传统的非线性函数相结合,提出了一种分段非线性函数,并通过仿真证明了其在不增加算法复杂度的情况下,大大降低了算法的分离误差；另一种是针对基于峭度符号估计的非线性函数中,通过峭度的符号选择非线性函数造成的信息遗漏的问题,引入了双曲-歌希模型,并将其与表示源信号信息的峭度相结合,提出了一种新的非线性函数,仿真结果表明,将改进的非线性函数用于自然梯度算法中,降低了算法的均方误差,提高了算法的分离精度。
[Abstract]:Blind source separation is the process of recovering the source signal only from the observed mixed signal without knowing the source signal and the prior information of the transmission channel.As one of the core algorithms of blind source separation, natural gradient algorithm has attracted more and more attention.At the same time, due to the advantages of natural gradient algorithm, such as low computational complexity, fast convergence speed and good separation effect, it has been widely used in the fields of speech signal processing, image processing, wireless communication and so on.This paper introduces the background and basic theory of blind source separation, discusses the solvability of blind source separation by introducing three basic models of blind source separation, and introduces several common cost functions from the point of view of optimization algorithm.The classical blind source separation algorithm, natural gradient algorithm, is introduced, the influence of nonlinear function on it is discussed, and the construction method of nonlinear function and the common nonlinear function are given.Aiming at some problems existing in the natural gradient blind source separation algorithm in instantaneous linear aliasing, especially the selection of nonlinear functions in the separation matrix with different homologous signals, two kinds of improved nonlinear functions are proposed.One is to solve the problem of the separation error caused by the same nonlinear function for all source signals in the traditional natural gradient algorithm. The Pearson system is introduced to combine the Pearson system with the traditional nonlinear function.A piecewise nonlinear function is proposed, and it is proved by simulation that the separation error of the algorithm is greatly reduced without increasing the complexity of the algorithm, and the other is aimed at the nonlinear function based on the kurtosis symbol estimation.Through the problem of information omission caused by the symbol selection of kurtosis, the hyperbolic-gog model is introduced, and a new nonlinear function is proposed by combining it with the kurtosis of the source signal. The simulation results show that,The improved nonlinear function is used in the natural gradient algorithm to reduce the mean square error of the algorithm and improve the separation accuracy of the algorithm.
【学位授予单位】：东北大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN911.7

【相似文献】