From Blind to Semi-Blind Acoustic Source Separation based on Independent Component Analysis

Typical acoustic scenes consist of multiple superimposed sources, where some of them represent desired signals, but often many of them are undesired sources, e.g., interferers or noise. Hence, source separation and extraction, i.e., the estimation of the desired source signals based on observed mixtures, is one of the central problems in audio signal processing. A promising class of approaches to address such problems is based on Independent Component Analysis (ICA an unsupervised machine learning technique. These methods enjoyed a lot of attention from the research community due to the small number of assumptions that have to be made about the considered problem. Furthermore, the resulting generalization ability to unseen acoustic conditions, their mathematical rigor and the simplicity of resulting algorithms have been appreciated by many researchers working in audio signal processing. However, knowledge about the acoustic scenario is often available and can be exploited to increase the performance of the source separation algorithm, e.g., the directions of arrival of the desired source signals relative to the observing microphone array. In this thesis, the problem of acoustic source separation and extraction is treated by Convolutive Blind Source Separation (CBSS) approaches based on ICA. As a basis for the thesis, we show and investigate relations between two well-known CBSS algorithms, Independent Vector Analysis (IVA) and TRIple-N Independent component analysis for CONvolutive mixtures (TRINICON) theoretically and experimentally in the first part. Here, a special focus lies on the exploitable properties of the respective source signals. A crucial aspect of Blind Source Separation (BSS) is the development of optimization schemes that allow for fast and computationally efficient iterative minimization of the BSS cost function. In the second part of the thesis, we focus on optimization approaches based on the Majorize-Minimize (MM) principle, analyze state-of-the-art methods and propose a new optimization approach originating from a negentropy perspective. The proposed algorithm exhibits an improved convergence rate relative to state-of-the-art approaches and is shown to be numerically stable and computationally efficient. The last part of the thesis is dedicated to the derivation of a framework for Semi-Blind Source Separation (SBSS), i.e., source separation that supports BSS methods with prior knowledge, from a Maximum A Posteriori (MAP) perspective. We demonstrate the use of this framework by incorporating spatial prior knowledge that enables a solution to the outer permutation ambiguity and allows to even address underdetermined problems. Finally, the integration of a Background (BG) model allows to deal with overdetermined situations and yields computationally efficient update schemes.