Overview of Source Separation

This chapter gives a general overview of the source separation problem and its underlying hypotheses, and of methods and algorithms for its solving, with an emphasis on the context of data processing in physical/chemical sensing applications. After explaining the motivations of source separation from the signal processing viewpoint, we present the mathematical formulation of the source separation problem, which can then be viewed as a matrix (or tensor) factorization model, for which there are essential indeterminacies. For achieving suitable solutions, it is necessary to assume priors on the source signals and on the mixing process. We especially focus on independent component analysis (ICA), a classical approach based on mutual statistical independence of the sources. We then give some examples of chemical and physical applications that can be formulated as source separation problems, and we provide a discussion on the main properties of the measurements and of the related mixing models. Then, we briefly present some separation approaches that can exploit these properties using various tools and methods which will be developed in the book. Finally, we describe the organization of the book and the notations used along all the chapters.