  In the context of Independent Component Analysis (ICA), noisy mixtures pose a
dilemma 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, optimal
Minimum 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 stationary
Gaussian sources in a semi-blind scenario, which conveniently lends itself to
either one of these objectives. We begin by deriving the ML Estimates (MLEs) of
the unknown (deterministic) parameters of the model: the mixing matrix and the
(possibly different) noise variances in each sensor. We derive the likelihood
equations for these parameters, as well as the corresponding Cram\'er-Rao lower
bound, and propose an iterative solution for obtaining the MLEs. Based on these
MLEs, the asymptotically-optimal "maximally separating" solution can be readily
obtained. However, we also present the ML-based MMSE estimate of the sources,
alongside a frequency-domain-based computationally efficient scheme, exploiting
their stationarity. We show that this estimate is asymptotically optimal and
attains 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. Empirical
results of three simulation experiments are presented, corroborating our
analytical derivations.
