Abstract

The notion of equivariance is relevant to source separation because multiplication of mixed signals is equivalent to changing the unknown parameter (the mixing matrix) into another mixing matrix. Elaborating on this observation, a wide class of batch estimators of the mixing matrix is first shown to offer uniform performance: quality of separation does not depend on the hardness of the mixture. Equivariance is next extended to adaptive algorithms, by the device of `serial updating'. Adaptive separators based on such a learning rule also exhibit uniform performance in a strong sense. I Introduction: Source separation Source separation, blind array processing, signal copy, independent component analysis, waveform preserving estimation: : : : these keywords refer to a signal model which is receiving increasing attention in both signal processing and neural network literature since the seminal paper [1]. This model is that of n statistically independent signals whose m (possibly noisy) l...

Citations

1036	Independent component analysis. a new concept - Comon - 1994
333	Blind beamforming for non-Gaussian signals - Cardoso, Souloumiac - 1993
146	Multidimensional independent component analysis - Cardoso
107	Separation of a mixture of independent sources through a maximum likelihood approach - Pham, Garrat, et al. - 1992
70	Robust learning algorithm for blind separation of signals - Cichocki, Unbehauen, et al. - 1994
53	Source separation without a priori knowledge: The maximum likelihood solution - Gaeta, Lacoume - 1990
35	B.Ans: “Detection de grandeurs primitives dans un message composite par une architecture de calcul neuromimetique en apprentissage non supervise”, X Colloque GRETSI - Jutten - 1985
24	The CM array: an adaptive beamformer for constant modulus signals - Gooch, Lundell
17	On the stability of source separation algorithms - Cardoso - 1998
13	Adaptive source separation without prewhitening - Laheld, Cardoso - 1994
6	Equivariant adaptive source separation," manuscript submitted to - Cardoso, Laheld - 1994
4	Testing statistical hypothesis. Wiley pub. in statistics - Lehmann - 1959