Traditional Blind Source Separation (BSS) methods require quite restrictive properties from the source signals (typically, statistically independent or at least uncorrelated sources) and mixing transform (typically, linear instantaneous mixtures). In this paper, we address a much more complex case, where the considered deterministic source signals may be correlated (we only request the source vectors and some associated vectors to be linearly independent) and where the mixing transform is nonlinear (more precisely, bilinear, which is e.g. of high interest for Earth observation applications). We propose a separation principle leading to a new set of BSS algorithms applicable to an arbitrary number of sources and based on nonlinear correlation parameters. Moreover, we analyze the separability properties of this approach and thus show that it is guaranteed to separate the sources up to the trivial scale and permutation indeterminacies.

Blind source separation; Dependent sources; Bilinear mixtures; Product proportionality separation principle