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

Bahram † Ehsandoust (1, 2) , Massoud † Babaie-Zadeh (2) , Bertrand Rivet (1) , Christian Jutten (1)

1 GIPSA-VIBS - GIPSA - Vision and Brain Signal Processing
2 EE department of SUT [Tehran] - Department of Electrical Engineering [Tehran]

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 the paper.

Mots clés: Blind Source Separation; Nonlinear Mixtures; Nonlinear Regression; Independent Component Analysis

Domaines: Traitement du signal et de l'image [eess.SP]

Bahram † Ehsandoust, Massoud † Babaie-Zadeh, Bertrand Rivet, Christian Jutten. Blind Source Separation in Nonlinear Mixtures: Separability and a Basic Algorithm. IEEE Transactions on Signal Processing, 2017, 65 (16), pp.4339 - 4352. ⟨10.1109/TSP.2017.2708025⟩. ⟨hal-01552273⟩