A general adaptive algorithm for nonGaussian source separation without any constraint

This paper deals with the blind source separation. The task consists in separating some independent and linearly mixed signals called sources. After some general remarks, the model is recalled and our approach based on the Maximum-Likelihood principle and on the higher-order statistics (HOS) is introduced. The main stages of the calculation are presented leading to the criterion of the separation based on a sum of squared cumulants of the sources at the fourth order. The second part is devoted to the adaptive implementation which is in opposition to the block treatment. The procedure using the gradient calculus is described. Some results obtained in simulations are shown, they correspond to the case of a mixture of two real valued sources. Finally, an example of a possible integration in a communications system based on multidimensional beamformers is briefly shown. But some tests on real data should be carried out beforehand.Peer ReviewedPostprint (published version

Overlearning in marginal distribution-based ICA: analysis and solutions

The present paper is written as a word of caution, with users of independent component analysis (ICA) in mind, to overlearning phenomena that are often observed.\\ We consider two types of overlearning, typical to high-order statistics based ICA. These algorithms can be seen to maximise the negentropy of the source estimates. The first kind of overlearning results in the generation of spike-like signals, if there are not enough samples in the data or there is a considerable amount of noise present. It is argued that, if the data has power spectrum characterised by $1/f$ curve, we face a more severe problem, which cannot be solved inside the strict ICA model. This overlearning is better characterised by bumps instead of spikes. Both overlearning types are demonstrated in the case of artificial signals as well as magnetoencephalograms (MEG). Several methods are suggested to circumvent both types, either by making the estimation of the ICA model more robust or by including further modelling of the data