Nonlinear independent component analysis by homomorphic transformation of the mixtures

Independent component analysis is often approached from an information theoretic perspective employing specific sample estimates for the mutual information between the separated outputs. These approximations involve the nonparametric estimation of signal entropies. The common approach involves the estimation of these quantities and adaptation based on these criteria. In contrast, in this paper, we propose a Gaussianization-based approach, where the separation is performed in two stages: Gaussianization of the mixtures using a homomorphic nonlinearity and separation of the independent components using principal component analysis (both stages possibly adaptive). Due to the rotation uncertainty in nonlinear ICA, the original sources cannot be recovered solely by the independence assumption. The proposed ICA methodology is applicable to instantaneous linear and nonlinear mixtures. The idea also generalizes easily to complex-valued nonlinear ICA.