Postnonlinear blind source separation via linearization identification

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Fabian J. Theis, Elmar Wolfgang Lang

Published: 2004, Last Modified: 13 Nov 2025IJCNN 2004EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: In the first part of the paper, the one-dimensional functional equation g(y(t))=cg(z(t)) with known functions y and z and constant c is studied. Its indeterminacies are calculated, and an algorithm for approximating g is proposed. Then, this linearization identification algorithm is applied to the postnonlinear blind source separation (BSS) problem. In the case of bounded sources, a self-organizing map is used to approximate the boundary, and the postnonlinearity estimation is reduced to the one-dimensional equation from above. For super Gaussian sources, the density maxima are interpolated by performing linear BSS within concentric rings. Postnonlinearity estimation using ring approximation separates the mixtures.