Single-channel source separation problems occur when a number of sources emit
signals that are mixed and recorded by a single sensor, and we are interested
in estimating the original source signals based on the recorded mixture. This
problem, which occurs in many sciences, is inherently under-determined and its
solution relies on making appropriate assumptions concerning the sources.
This dissertation is concerned with model-based probabilistic single-channel
source separation based on non-negative matrix factorization, and consists of
two parts: i) three introductory chapters and ii) five published papers. The
first part introduces the single-channel source separation problem as well as
non-negative matrix factorization and provides a comprehensive review of existing
approaches, applications, and practical algorithms. This serves to provide
context for the second part, the published papers, in which a number of methods
for single-channel source separation based on non-negative matrix factorization
are presented. In the papers, the methods are applied to separating audio signals
such as speech and musical instruments and separating different types of
tissue in chemical shift imaging.