计算机科学 ›› 2014, Vol. 41 ›› Issue (12): 78-81.doi: 10.11896/j.issn.1002-137X.2014.12.017

• 网络与通信 • 上一篇    下一篇

基于Givens变换矩阵的时间结构信号盲源分离新算法

赵礼翔,刘国庆   

  1. 南京工业大学电子与信息工程学院 南京211816;南京工业大学理学院 南京211816
  • 出版日期:2018-11-14 发布日期:2018-11-14
  • 基金资助:
    本文受江苏省自然科学基金(BK2011238),南京气象雷达开放实验室研究基金(BJG201103)资助

Novel Algorithm of Blind Source Separation with Temporal Structure Based on Givens Transformation Matrix

ZHAO Li-xiang and LIU Guo-qing   

  • Online:2018-11-14 Published:2018-11-14

摘要: 对于时间结构信号的盲源分离(Blind Source Separation,BSS),独立成分分析(Independent Component Analysis,ICA)是十分有效的方法。在对观测信号白化处理后,ICA的关键是寻找去除高阶相关性的正交分离矩阵。鉴于任意维数正交矩阵可以表示为Givens变换矩阵的乘积,提出了一种新的时间结构信号盲源分离算法。首先,利用Givens变换矩阵参数化表示正交分离矩阵,减少了要估计参数的个数;其次,以多步时延协方差矩阵的联合近似对角化为目标函数,将盲源分离问题转化为无约束优化问题,并利用拟牛顿法中的BFGS算法对Givens变换矩阵中的参数进行估计,得到分离矩阵;最后,以实际的混合语音信号分离做仿真实验,验证了该算法对时间结构信号的盲源分离是有效的。

关键词: 盲源分离,时间结构,独立成分分析,正交矩阵,Givens变换矩阵

Abstract: Independent Component Analysis (ICA) is an efficient method to solve the Blind Source Separation (BSS) problem with temporal structure.The key to ICA for whiten observation signals is to find an orthogonal matrix to throw away high-order redundancy between components.Given this problem,we proposed the parametric representation of orthogonal matrix in arbitrary dimension using Givens transformation matrix.Based on this,a new separation algorithm was proposed.Firstly,we decreased the number of parameters to be estimated by parameterizing the orthogonal matrix using Givens transformation matrix.Secondly,we converted the BSS problem into an unconstrained optimization problem,where the object function is the joint approximate diagonalization of multistep delayed covariance matrices.In order to estimate the parameters in orthogonal matrix,BFGS algorithm of quasi-Newton method was provided solving the unconstrained optimization problem.Finally,the separation for real mixed voice signals shows the effectiveness of our algorithm.

Key words: Blind source separation,Temporal structure,Independent component analysis,Orthogonal matrix,Givens transformation matrix

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