Separation of Nonlinearly Mixed Sources Using End-to-End Deep Neural Networks

In this letter, we consider the problem of blind source separation under certain nonlinear mixing conditions using a deep learning approach. Conventionally, the separation of sources within linear mixtures is achieved by applying the independence property of the sources. In the nonlinear regime, however, this property is no longer sufficient. In this letter, we consider nonlinear mixing operators where the non-linearity could be fairly approximated using a Taylor series. Next, for solving the nonlinear BSS problem, we design an end-to-end recurrent neural network (RNN) that learns the inverse of the system, and ultimately separates the sources. For training the RNN, we employ a set of multi-variate polynomial functions to simulate the Taylor expansion of the nonlinear mixture. Numerical experiments show that the proposed method successfully separates the sources with a performance superior to the state of the art approaches.