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In the context of Independent Component Analysis (ICA), noisy mixtures pose adilemma regarding the desired objective. On one hand, a "maximally separating"solution, providing the minimal attainable Interference-to-Source-Ratio (ISR),would often suffer from significant residual noise. On the other hand, optimalMinimum Mean Square Error (MMSE) estimation would yield estimates which are the"closest possible" to the true sources, often at the cost of compromised ISR.In this work, we consider noisy mixtures of temporally-diverse stationaryGaussian sources in a semi-blind scenario, which conveniently lends itself toeither one of these objectives. We begin by deriving the ML Estimates (MLEs) ofthe unknown (deterministic) parameters of the model: the mixing matrix and the(possibly different) noise variances in each sensor. We derive the likelihoodequations for these parameters, as well as the corresponding Cram\'er-Rao lowerbound, and propose an iterative solution for obtaining the MLEs. Based on theseMLEs, the asymptotically-optimal "maximally separating" solution can be readilyobtained. However, we also present the ML-based MMSE estimate of the sources,alongside a frequency-domain-based computationally efficient scheme, exploitingtheir stationarity. We show that this estimate is asymptotically optimal andattains the (oracle) MMSE lower bound. Furthermore, for non-Gaussian signals,we show that this estimate serves as a Quasi ML (QML)-based Linear MMSE (LMMSE)estimate, and attains the (oracle) LMMSE lower bound asymptotically. Empiricalresults of three simulation experiments are presented, corroborating ouranalytical derivations.

A Maximum Likelihood-Based Minimum Mean Square Error Separation and Estimation of Stationary Gaussian Sources from Noisy Mixtures