| Summary: | Blind source separation (BSS) techniques have the aim of separating original source signals from their mixtures without having or with a little knowledge about the source signals or the mixing process. Tensor based source separation techniques have become increasingly popular for various applications since they exploit different inherent diversities of the sources. Therefore, they can improve the estimation of desired sources and the identification of the mixing system. The proposed techniques in this thesis are the extensions of conventional tensor factorisation techniques. Our proposed methods can be categorised in two groups; single and multichannel source separation techniques. For single channel source separation a tensor based singular spectrum analysis (SSA) is proposed followed by a way to select the desired subspaces automatically. The proposed method is compared with conventional methods using both synthetic and real electroencephalography (EEG) sleep data to track different sleep stages. Another proposed method is symmetric tensor decomposition. The method has been applied to detect the beta rebound, as an indicator of movement related brain responses, in brain computer interfacing (BCI). In addition to single channel source separation, several multichannel BSS techniques have been proposed. The first method is a constrained BSS technique which uses the spatial information of data to improve the performance. This approach is particularly useful in separation of weak intermittent signal components. The results show that the proposed method performs better than the existing methods in terms of accuracy and quality. Complex tensor factorisation of correlated brain sources is attempted as well. The electrical brain responses due to motory, sensory, or cognitive stimuli, i.e. event related potentials (ERPs), particularly P300, have been used for cognitive information processing. P300 has two subcomponents, P3a and P3b, which are correlated, and therefore, the traditional BSS approaches fail in their separation. A complex-valued tensor factorisation of EEG signals is introduced with the aim of separating P300 subcomponents. The proposed method uses complex-valued statistics to exploit the data correlation. In this way, the variations of P3a and p3b can be tracked for the assessment of the brain state. The results of this work are compared with those of spatial principle component analysis (SPCA) method. Communication signals such as quadrature-phase shift keying (QPSK) often pose as complex waveforms and suffer from multipath and clutter problems. In this thesis therefore, a new convolutive complex tensor factorisation system is proposed to recover such signals in the receiver and estimate the communication channels. The proposed method is evaluated using simulated data with multiple multi-paths and various non-circularity and noise levels. Simulation results confirm the superiority of the proposed method over the existing popular techniques.
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