| Blind Source Separation(BSS)is a classical problem in signal processing with a wide range of applications in many fields.However,the Underdetermined Blind Source Separation(UBSS)problem is more generic since the number of acquisition devices is usually less than the number of source signals.UBSS is more realistic and challenging.Therefore,it is of great significance to researching on UBSS.This paper mainly explore the separation signal algorithm for a class of UBSS problem.It is introduced about the basic theory of K-means Clustering algorithm and Rational Function ICA algorithm for Blind Source Separation.K-means Clustering algorithm is one of the top ten data mining algorithms.Given the number of clusters,it can divide samples into different categories according to the similarity.The Rational Function ICA algorithm is aimed at the BSS problem where the number of mixed signals is equal to that of source signals.This method can separate signals effectively by applying a rational function and avoids the selection process of switching functions.Here are three main aspects in this paper:Part I: The K-C-means algorithm,adaptive K-C-means algorithm and accurate K-C-means algorithm are proposed in view of K-means algorithm's shortcomings which include the number of clustering needs to be given in advance,the choice of initial clustering centers has great influence on the clustering result and outliers have great influence on the clustering center of each iteration.Numerical experiments show that the improved clustering algorithms are suitable for solving our problems.Part Ⅱ: A method for a simple case of UBSS is presented in which only one person speaks at a time interval.By analyzing the relationship between the rows of two observation signals,the linear mixed signals can be separated.Part Ⅲ: The Rational Function ICA algorithm for UBSS is proposed for another case: the number of source signals is no more than that of mixed signals in each given time interval.And the Rational Function ICA algorithm for BSS is used to solve this problem at each given time interval.The numerical results show that our method can effectively separate the source signals.The first chapter mainly introduces the basic theory of K-means Clustering algorithm and its improvements.A method for solving a simple case of UBSS is introduced in the second chapter.The third chapter introduces the Rational Function ICA algorithm for UBSS in which the number of source signals is no more than that of mixed signals in each given time interval.The numerical experiments are shown in the fourth chapter.The summaries and prospects are given in the last part. |
