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Blind source separation of sparse sources with attenuations and delays : a novel approach for the under-determined case Saab, Rayan

Abstract

Separation of sources is an important problem in signal processing where one tries to extract two or more underlying signals from their recorded mixtures. Blind source separation is the problem of extracting sources armed only with the knowledge of the observable mixtures and necessarily, some assumptions on the underlying sources or their statistics. Applications of blind source separation abound, from EEG and fMRI in the field of neuroscience, to speech and audio recognition and separation, to face recognition, financial series analysis and communications. In this thesis we explore blind source separation in the case where there are more sources than available mixtures, i.e. the under-determined case. We take into account both attenuations and delays in the mixing process, utilizing sparsity of the sources for demixing. We provide the theoretical framework for source separation and present simulation results to validate our method. There are existing techniques that solve the blind source separation problem for instantaneous under-determined mixtures, and ones that solve the anechoic under-determined problem for two mixtures only. The proposed technique is novel in that it is the first to solve the blind source separation problem in a general anechoic setting where no restrictions are put on the number of mixtures, and no assumptions are made on the number of sources.

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