Determination of the Number of Source Signals in Blind Source Separation

摘要

The determination of the number of unknown source signals when there are fewer sources than mixtures in blind source separation (BSS) has always been an unsolved problem. In the current paper, it is demonstrated that the source number can be estimated by computing the rank of the data matrix of the mixed signals. However, in the presence of noise, this simple conclusion will no longer hold. In order to solve this problem, we further prove that the number f sources can also be estimated reliably by computing the effective rank of correlation matrix of the signal mixtures by means of singular value decomposition, and present a simple algorithm. It paves the way to wider applications of BSS methods to real world signal processing.