An Information-Maximization Approach to Blind Separation and Blind Deconvolution

TLDR

Information maximization in nonlinear networks has properties absent in linear cases, as noted by Linsker (1989). The study derives a self‑organizing learning algorithm that maximizes information transfer in nonlinear unit networks. The algorithm, defined for the zero‑noise limit and agnostic to input distributions, uses nonlinear transfer functions to capture higher‑order moments and achieve redundancy reduction among output units. The algorithm successfully separates independent components, isolates up to ten speakers in cocktail‑party mixtures, performs blind deconvolution of echoes, and its information‑transfer dynamics depend on time delays, supporting a unifying framework for blind signal processing.

Abstract

We derive a new self-organizing learning algorithm that maximizes the information transferred in a network of nonlinear units. The algorithm does not assume any knowledge of the input distributions, and is defined here for the zero-noise limit. Under these conditions, information maximization has extra properties not found in the linear case (Linsker 1989). The nonlinearities in the transfer function are able to pick up higher-order moments of the input distributions and perform something akin to true redundancy reduction between units in the output representation. This enables the network to separate statistically independent components in the inputs: a higher-order generalization of principal components analysis. We apply the network to the source separation (or cocktail party) problem, successfully separating unknown mixtures of up to 10 speakers. We also show that a variant on the network architecture is able to perform blind deconvolution (cancellation of unknown echoes and reverberation in a speech signal). Finally, we derive dependencies of information transfer on time delays. We suggest that information maximization provides a unifying framework for problems in "blind" signal processing.