Blind Source Separation in Nonlinear Mixtures: Separability and a Basic Algorithm

• Published in: IEEE transactions on signal processing Vol. 65; no. 16; pp. 4339 - 4352
• Main Authors: Ehsandoust, Bahram, Babaie-Zadeh, Massoud, Rivet, Bertrand, Jutten, Christian
• Format: Journal Article
• Language: English
• Published: IEEE 15.08.2017; Institute of Electrical and Electronics Engineers
• Subjects: Blind source separation; Computer Science; independent component analysis; Jacobian matrices; nonlinear mixtures; nonlinear regression; Random processes; Random variables; Signal and Image Processing; Signal processing algorithms; Stochastic processes; Blind Source Separation; Nonlinear Regression; Independent Component Analysis; Nonlinear Mixtures
• ISSN: 1053-587X; 1941-0476; 1941-0476
• DOI: 10.1109/TSP.2017.2708025

In this paper, a novel approach for performing blind source separation (BSS) in nonlinear mixtures is proposed, and their separability is studied. It is shown that this problem can be solved under a few assumptions, which are satisfied in most practical applications. The main idea can be considered as transforming a time-invariant nonlinear BSS problem to local linear ones varying along the time, using the derivatives of both sources and observations. Taking into account the proposed idea, numerous algorithms can be developed performing the separation. In this regard, an algorithm, supported by simulation results, is also proposed in this paper. It can be seen that the algorithm well separates the mixed sources, however, as the conventional linear BSS methods, the nonlinear BSS suffers from ambiguities, which are discussed in this paper.