Abstract
Equivariant adaptive separation via independence (EASI) is one of the most successful algorithms for blind source separation (BSS). However, the user has to choose non-linearities, and usually simple (but non-optimal) cubic polynomials are applied. In this paper, the optimal choice of these non-linearities is addressed. We show that this optimal non-linearity is the output score function difference (SFD). Contrary to simple non-linearities usually used in EASI (such as cubic polynomials), the optimal choice is neither component-wise nor fixed: it is a multivariate function which depends on the output distributions. Finally, we derive three adaptive algorithms for estimating the SFD and achieving “quasi-optimal” EASI algorithms, whose separation performance is much better than “standard” EASI and which especially converges for any sources.
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