| Summary: | Blind Source Separation (BSS) methods have been attracting increasing attention for their promising applications in signal processing. Despite recent progress on the research of BSS, there are still remaining challenges. Specifically, this dissertation focuses on developing novel Underdetermined Blind Source Separation (UBSS) methods that can deal with several specific challenges in real applications, including limited number of observations, self/cross dependence information and source inference in the underdetermined case. First, by taking advantage of the
Noise Assisted Multivariate Empirical Mode Decomposition (NAMEMD) and Multiset Canonical Correlation Analysis (MCCA), we propose a novel BSS framework and apply it to extract the heart beat signal form noisy nano-sensor signals. Furthermore, we generalize the idea of (over)determined joint BSS to that of the underdetermined case. We explore the dependence information between two datasets and propose an underdetermined joint BSS method for two datasets, termed as UJBSS-2. In addition, by exploiting the cross correlation between each pair of datasets, we develop a novel and effective method to jointly estimate the mixing matrices
from multiple datasets, referred to as Underdetermined Joint Blind Source Separation for Multiple Datasets (UJBSS-M). In order to improve the time efficiency and relax the sparsity constraint, we recover the latent sources based on subspace representation when the mixing matrices are estimated. As an example application for noise enhanced signal processing, the proposed UJBSS-M method also can be utilized to solve the single-set UBSS problem when suitable noise is added to the observations. Finally, considering the recent increasing need for biomedical signal processing in the ambulatory environment, we propose a novel UBSS method for removing electromyogram (EMG) from Electroencephalography (EEG) signals. The proposed method for recovering the underlying sources is also applicable to other artifact removal problems. Simulation results demonstrate that the proposed methods yield superior performances over conventional approaches. We also evaluate the proposed methods on real physiological data, and the proposed methods are shown to effectively and efficiently recover the underlying sources. === Applied Science, Faculty of === Electrical and Computer Engineering, Department of === Graduate
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