Blind signal processing by complex domain adaptive spline neural networks

In this paper, neural networks based on an adaptive nonlinear function suitable for both blind complex time domain signal separation and blind frequency domain signal deconvolution, are presented. This activation function, whose shape is modified during learning, is based on a couple of spline functions, one for the real and one for the imaginary part of the input. The shape control points are adaptively changed using gradient-based techniques. B-splines are used, because they allow to impose only simple constraints on the control parameters in order to ensure a monotonously increasing characteristic. This new adaptive function is then applied to the outputs of a one-layer neural network in order to separate complex signals from mixtures by maximizing the entropy of the function outputs. We derive a simple form of the adaptation algorithm and present some experimental results that demonstrate the effectiveness of the proposed method.