A blind-ML scheme for blind source separation
Yuval Lomnitz, Arie Yeredor · 2003
We present a new approach to the blind source separation problem (BSS, also known as Independent Component Analysis (ICA)), which we term ”Blind-ML”. This approach proposes a framework for estimation of the mixing, which combines a possibly non-parametric distribution estimator with the maximum likelihood estimation of the separating matrix, thereby obtaining both robustness to the sources’ densities, and asymptotic efficiency. We provide guidelines for a proof, and verify using simulations, that this approach yields asymptotically efficient (optimal) mean-square-error performance without knowledge of the source densities, and with mild assumptions on the types of sources. asymptotically efficient estimation scheme, whose optimality will not depend on the source densities. 2. A LOWER BOUND FOR MSE (CRLB) The Cramér Rao Lower Bound (CRLB) for the mean-square error (MSE) in unbiased estimation of the separating matrix when the sources ’ densities are known, has been calculated in [1]. Here we present the bound in terms of the off-diagonal "$#&% ' elements of the ”contamination matrix”