Blind deconvolution of EEG signals using the stochastic calculus

A new tool, in the blind deconvolution, for the estimation of both the source signals and the unknown channel dynamics has been developed. The framework for this methodology is based on a multi-channel blind deconvolution technique that has been reformulated to use Stochastic Calculus. The convolution processes is modeled as Finite Impulse Response (FIR) filters with unknown coefficients. Assuming that one of the FIR filter coefficients is time-varying, we have been able to get accurate estimation results for the source signals, even though the filter order is unknown. The time-varying filter coefficient was assumed to be a stochastic process. A stochastic differential equation (SDE), with some unknown parameters, was developed that described its evolution over time. The SDE parameters have been estimated using methods in stochastic calculus. The method was applied to the problem of two chatting persons and the problem of EEG contaminated by EOG. Comparisons to existing methods are also reported.