Underdetemined Blind Source Separation And Application For Signal Extraction

The signal received from complex background is often a mixture of many signals generated by different sources. For example, audio signal received by microphone; data in sonar array and communication signal processing; bioelectrical signal detected by multi sensors. Separating one signal from the mixture is a traditional task in signal processing, but if the mix mode is unknown, this task will become a hard problem that is generally called blind source separation (BSS).With a fast development, BSS problem turns to be a research focus in signal processing and neural network areas. BSS means, with little prior knowledge about signal sources and mix mode, given only the observe signals, to estimate or recover original signals. But many classical BSS algorithms such as independent component analysis (ICA) and its extending algorithms are all based on a main assumption that the number of observe signals must be no less than that of original signals. On one hand, this assumption doesn't match the word 'blind', and on the other hand, it's hard to be satisfied in practice. So the underdetermined situation is significant and universal.In this thesis, two solutions to the underdetermined BSS problem are proposed from different aspects. First, based on classical BSS algorithms ICA method, using empirical model decomposition (EMD) to construct reference signal to ensure the assumption mentioned above. A new model structure is found and applied in single evoked potential (EP) signal few-trial extraction successfully. Second, sparse component analysis (SCA) algorithm is well studied. Using sparse decomposition, a new SCA algorithm based on expectation maximization (EM) and principal components analysis (PCA) is proposed to solve the problem of underdetermined BSS. Then the algorithm is applied for blind separation of audio signals. The performances of these solutions are demonstrated by lots of simulations, and the new algorithm can be widely used in practice.Furthermore, non-negative matrix factorization (NMF) and application for BSS are studied.