基于相似性函数的稀疏成分分析混合矩阵估计方法  

Estimating the Mixing Matrix Based on a Similarity Function in Sparse Component Analysis

作　　者：徐旭[1] 郭崇慧[2] 

机构地区：[1]大连理工大学数学科学学院,大连116024 [2]大连理工大学系统工程研究所,大连116024

出　　处：《工程数学学报》2013年第5期642-654,共13页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(70871015;71171030);新世纪优秀人才支持计划(NCET-11-0050)~~

摘　　要：稀疏成分分析是信号处理中解决欠定盲源分离问题的新方法,本文研究了稀疏成分分析中的混合矩阵估计问题,提出了无需预知源个数利用一种相似性函数估计混合矩阵的方法.首先,估计相似性函数中的核参数,使得算法适应不同的稀疏信号.然后,给出了估计混合矩阵的不动点算法.最后,实验结果表明提出的算法通过适当地选取参数,能够准确有效地估计出具有不同源个数的混合矩阵,对不太稀疏的源也有令人满意的结果.Sparse component analysis is a new approach to solve the problem of underde- termined blind source separation in signal processing area. In this paper, a clustering method based on similarity function is developed to estimate the mixing matrix in the case of unknowing the number of source signals. Firstly, the kernel parameter of similarity function is estimated so that the proposed algorithm adapts to different kinds of sparse signals. Then, a fixed point algorithm is formulated to estimate the mixing matrix. Finally, the simulations show that through choosing parameters appropriately, our algorithm effectively and accurately estimates the mixing matrix with different numbers of sources. The results for insufficient sparsity sources is also satisfactory.

关 键 词：稀疏成分分析 欠定盲源分离 相似性函数 不动点算法 凝聚层次聚类 

分 类 号：TN911[电子电信—通信与信息系统]