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

Author

Macchi, Odile ; Moreau, Eric

Author_Institution

Lab. des Signaux et Syst., CNRS, Gif-sur-Yvette, France

Volume

45

Issue

4

fYear

1997

fDate

4/1/1997 12:00:00 AM

Firstpage

918

Lastpage

926

Abstract

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

Keywords

adaptive signal processing; convergence of numerical methods; linear network analysis; recurrent neural nets; signal processing; Herault-Jutten algorithm; convergence analysis; convergent algorithm; direct linear network; equilibrium points; feedback linear neural network; implementation constraints; linear mixture; nonGaussian independent sources; quasiquadratic mean; self-adaptive rule; self-adaptive source separation; separating states; stability status; step size; stochastic algorithm; Airports; Algorithm design and analysis; Array signal processing; Convergence; Inverse problems; Linear feedback control systems; Neural networks; Neurofeedback; Source separation; Stability;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.564180

Filename

564180