On the relation between ICA and MMSE based source separation

This paper aims at deriving a relationship between minimum mean square error (MMSE) based source separation and independent component analysis (ICA) based on the Kullback-Leibler divergence (KLD) for a linear noisy mixing model. Starting from a description of the demixing task and two well-known solutions, inverse mixing matrix and MMSE solution, we derive an analytic expression for the demixing matrix of KLD-based ICA in the presence of noise. The derivation is done by using a perturbation analysis valid for small noise variance. Furthermore, we provide an analytic expression for the mean square error (MSE) of the demixed signals using KLD-based ICA. We show that for a wide range of the shape parameter of the generalized Gaussian distribution (GGD), the MSE of KLD-based ICA is very close to the MMSE. Simulations verify this and show that in practice the variance of the ICA estimation due to limited amount of data also influences the achievable performance.