Extracting post-nonlinear signal with specific kurtosis range

Blind source extraction (BSE) is an important technique to extract a desired source from the mixed signals and the post-nonlinear (PNL) mixture is more realistic model in many situations. In this paper, we address the problem of extracting the source of interest from the PNL mixture. First, the prior knowledge about the desired source, such as its normalized kurtosis range, can be treated as a constraint and incorporated into the contrast function. Therefore, BSE from the PNL mixture can be formulated a constrained optimization problem. Second, the inverse of the unknown nonlinear function is approximated by the multi-layer perceptions (MLP) network because neural network can uniformly approximate any continuous function if there is sufficient number of neurons in the hidden layer. Finally, the source of interest can be extracted from the PNL mixture by minimizing the constrained optimization problem with standard gradient descent method. Extensive computer simulations and experiments demonstrate the validity of our algorithm.