Underdetermined Blind Source Separation and Its Application

Blind source separation(BSS) is a new domain of signal processing, it is also a hot spotlight of application. It refers to information theory, neural network, statistic signal processing, optimization theory and so on. Recently, the research on blind source separation is paid attention to and explored deeply and widely home and abroad, and its theories and applications are developed widely.

In reality, the signal we received is often a mixture of many signals generated by different sources. For example, cocktail party problem, EP signal extraction problem, and so on. Blind source separation is, with little prior knowledge about signal sources and mix mode, given only the observed signals, to estimate or recover original signals. In this paper classic ICA algorithms are researched. Classic ICA algorithms, such as FastICA, Infomax, JADE etc, are based on the assumption that the number of observed signals must be no less than that of original signals.

Through comparison to the simulation experimental results for the situation that the number of observed signals is no less than that of original signals, FastICA, Infomax, JADE get good results. The advantages of FastICA are faster convergence, able to extract components individually, simple computing. The situation that the number of observed signals is less than that of original signals, namely underdetermined BSS, is a hotspot and difficult spot.

We also explores underdetermined BSS, and does research on the speech signal satisfied sparseness and EP signal not satisfied sparseness, gets the estimated signals of source by simulation. The speech signals not satisfied sparseness in time domain is transformed to transformed domain so that we can get the estimation of sources. For the extraction of EP signal with single-trail in single channel, because EP signal is not satisfied sparseness, traditional underdetermined BSS algorithms can not be used. This paper extracts EP signal with single-trail in single channel through PCA processing, with EMD, gets the pre-estimated signals, through algorithm derivation and founding a model, gets the EP with single-trail in single channel.