Self-adaptive source separation .I. Convergence analysis of a direct linear network controlled by the Herault-Jutten algorithm

It is known that self-adaptive separation of a linear mixture of non-Gaussian independent sources can be achieved with a feedback linear neural network that is adapted by the Herault-Jutten (1991) algorithm. Yet, realizability of the feedback requires implementation constraints. An equivalent direct (without feedback) network is considered that is free of these constraints while the self-adaptive rule is kept unchanged. The separating states are shown to be equilibrium points. Their stability status is studied in the case of two sources. Then, we show that the algorithm is convergent in the "quasi"-quadratic mean sense toward a separating state for a small enough step-size.