Separation of post-nonlinear mixtures using ACE and temporal decorrelation
ABSTRACTWe propose an efﬁcient method based on the concept ofmaximal correlation that reduces the post-nonlinear blindsource separation problem (PNL BSS) to a linear BSS prob-lem. For this we apply the Alternating Conditional Expec-tation (ACE) algorithm – a powerful technique from non-parametricstatistics –toapproximatelyinvertthe (post-)non-linear functions. Interestingly, in the framework of the ACEmethod convergence can be proven and in the PNL BSSscenario the optimal transformation found by ACE will co-incide with the desired inverse functions. After the non-linearities have been removed by ACE, temporal decorrela-tion (TD) allows us to recover the source signals. An ex-cellent performance underlines the validity of our approachand demonstrates the ACE-TD method on realistic exam-ples.1. INTRODUCTIONBlind source separation (BSS) research has mainly beenfocused on variants of linear ICA and temporal decorrela-tion methods (see e.g. [14, 6, 5, 7, 1, 2, 13, 29, 22, 12]).Linear BSS assumes that at time