Nonlinear inverse filtering in the presence of noise

In an earlier paper we have considered the problem of separating signals from an additive mixture with nonlinear (chaotic) noise. Our approach has been based on an understanding of the effect of linear filters on nonlinear processes. In particular, we were able to demonstrate the usefulness, in this context, of nonlinear filters which act as the inverse of given linear filters. In this paper we extend this work by investigating the effects of stochastic noise on these methods. We discuss the robustness of the inverse filters in the presence of noise, and describe how nonlinear noise reduction methods developed for chaotic systems can be used in conjunction with inverse filters to improve the signal separation when stochastic noise is present. We illustrate this discussion with a synthetic example using speech data.