New Tensor Factorization Based Approaches For Blind Source Separation.

Blind source separation (BSS), aimed at estimation of original source signals from their mixtures without any (or with minor) knowledge about the sources or the mixing medium, is an exciting area of research due to its various applications. Recently, tensor factorization (TF) has been employed for blind modelling of biomedical data to estimate the signatures of desired sources and identify the mixing system by factorizing the second/higher order statistics of the mixtures. Our proposed approaches in this thesis extend the conventional TF methods to exploit nonstationarity of the sources in developing new BSS methodologies. For instantaneous mixtures, we propose a novel, so called, first order blind source separation (FOBSS) method to factorize the mixture signals. This method has been used for separation of EEG and linear mixtures of speech signals and has higher accuracy and robustness in both separation and identification of moderately correlated sources. The FOBSS method is then extended for separation of mutually correlated subcomponents (P3a and P3b) of event related potentials (ERPs). In the case of having nonstationary sources with sparse events, a new TF based underdetermined BSS is developed which exploits block sparsity of the sources. This method overcomes the traditional bounds for the maximum number of separable sources in the context of TF. This method, called UOM-BSS, has been used for separation of synthetic and real block sparse signals such as speech. In addition, with regards to convolutive mixtures, a novel TF based convolutive BSS (CBSS) method has been developed, in time domain, by proposing an extended version of FOBSS for separation of sources with sparse events. This method has been applied for separation of heart and lung sound signals form their convolutive mixtures. Finally, a semi-blind version of proposed TF CBSS is introduced. This method has been applied for separation of speech signals when some a priori information about the locations of the speakers and the microphones are available. The results demonstrate the higher performance of the semi-blind method compared with those of blind CBSS