Blind Separation of Linear Convolutive Mixtures through Parallel Stochastic Optimization

We apply stochastic parallel optimization techniques to on-line blind separation of linear convolutive mixtures of independent time-varying signals. The optimization performs stochastic gradient descent on a scalar measure of statistical independence observed directly on the outputs of the unmixing network, which contains a matrix of finite impulse response (FIR) filters. We derive on-line adaptation rules, and a scalable modular architecture with minimum memory requirements amenable to parallel VLSI implementation. The architecture implements a slight modification of the network adaptation rule, which omits symmetrical non-causal terms in the computation of the stochastic gradient. Simulations indicate near-perfect separation using both versions of the rule, with a minimum phase response resulting from the simplified version.