Breaking Up is Hard to Do: Blind Signal Separation

In \blind signal separation," a collection of linear combinations of signals is broken into its original sources without any knowledge of their initial characteristics. In this paper, we review four important yet fundamentally diierent approaches to this problem. An algorithm by Herault and Jutten emulates structures found in biological systems through a recursive adaptive neural network. In JADE and EFOBI, Principle Components Analysis (PCA) is extended with fourth-order statistical matrix diagonal-ization. AMUSE has a similar extension of PCA, but followed by a temporal variance matrix diagonalization, leading to a diierent set of requirements for identiiability. We describe these algorithms under the same notational framework, and clearly list their underlying probabilistic assumptions.