On blind source separation under exotic data structures

Blind source separation techniques form a wide class of approaches designed to uncover latent sources of interest, when only mixtures of them are available. The premise is that we have only a little information concerning the mixing system and the underlying latent sources. Recent technological advances have increased the demand of blind source separation approaches in exotic setups. In particular, we consider blind source separation for complex-valued data and for tensor-valued data. Furthermore, we consider approaches for measuring the performance of different blind source separation procedures in controlled simulation setups. The topics of this dissertation vary from theoretical to very applied: (1) We provide theoretical foundations for solving and identifying solutions under different blind source separation models and derive corresponding asymptotic properties. (2) We greatly extend the applicability of a performance measure designed for blind source separation and again provide corresponding asymptotic properties. (3) We consider algorithmic approaches and provide new practical ways to estimate latent sources of interest. (4) We successfully apply a blind source separation method to uncover interesting structure from a real-life cancer incidence data. The unifying factor between the different topics is blind source separation. In addition, these topics are extended to cover specific exotic setups. These exotic extensions are not derived for the sake of academic interest only, they are always motivated by the demand of real-life applications.