Blind Source Separation and Applications

Post-non linear mixtures are associated to models where a linear mixing system is followed by component wise memory less distortions. For instance, such mixtures occurs when the propagation in the channel is linear and the sensors can be nonlinear. Two theoretical results concerning the separability of this class of nonlinear mixtures has been developed in the project. Moreover, the results have been generalized to convolutive post-nonlinear mixtures, in which the propagation in the channel involves filtering. Theoretical tools, like fast multivariate score function estimation, have been developed for practically implementing these methods. Softwares and demo are publicly available on the Bliss Web pages : http://www.lis.inpg.fr/pages_perso/bliss/ Currently, we are working for validating these methods on actual post-nonlinear mixtures, e.g. on smart chemical sensor arrays based on ISSFET and on image processing.

The Bayes group in the Laboratory of Computer and Information Science and Neural Networks Research Centre in Helsinki University of Technology, Espoo, Finland has developed Bayesian methods, which are suitable for unsupervised learning. We have studied Bayesian ensemble learning, which is one type of variational Bayesian learning, and applied it to various latent variable model structures. In particular, in the BLISS project we have introduced and studied variational Bayesian methods for blind source separation of nonlinear, non-independent, and dynamic mixtures. A major research line is development of modular building blocks which can be used for constructing nonlinear and non-Gaussian model and which allow automated derivation of learning rules. We have successfully applied our methods to various real-world data sets. In particular, we have released several free software packages, which are available on the home page of the Bayes group http://www.cis.hut.fi/projects/bayes/. There are also selected most important publications. The main results achieved have been reported in the deliverables of the BLISS project. Bayesian data analysis was listed among the 10 most promising areas of new technology in a respected technological review in 2004. Thus the results achieved have a wide application potential to various data analysis and modeling problems. We have already applied our methods to analysis of video image sequences, astronomical images, color description, speech data, biomedical MEG data, and control problems, as well as to reconstruction of missing values in various data sets. For more details, see the publications, which can be found on our home page.

We have developed a method for blind separation of convolutive mixtures, which exploits the non stationarity of the source signals. The method works on in the frequency domain so that it can handle mixing filters with quite long impulse responses. It is thus quite suitable for the separation of audio mixtures, as such mixtures can result from filters with quite long impulse response in a reverberrant environment, and the audio signals are highly nonstationary. The principal difficulty in a frequency domain approach is the frequency permutation ambiguity problem. Novel methods have been developed to solve this problem.

During the life of the BLISS project, we have contributed to making biomedical signal processing possibly the most successful field of application for independent component analysis (ICA). To this end, we have addressed the issues of artifact identification and reduction from electro- and magnetoencephalograms (EEG and MEG, respectively), as well as from functional magnetic resonance images (fMRI). A sign of its success is the wide acceptance of ICA by the medical community, with whom we kept active collaborations. Practical implications to human brain mapping, or to clinical use of EEG, MEG and fMRI are considerable. Furthermore, with a clear target in neuroscience, we have analysed brain responses, evoked by external stimuli, both in an MEG and fMRI mapping modalities. Results lead into innovative insights to human brain mapping. The extension of the applications of ICA, from standard EEG and MEG to other measuring techniques, was as well addressed. To this end, we studied DC-Magnetometry; performed brain tissue segmentation and classification, using structural MRI; analysed the hemodynamic response of the brain to auditory stimuli, via fMRI; addressed the non invasive fetal electrocardiogram (fECG) extraction using surface electrodes.

We develop a method taking into account the Markovian property of sources, which is more general, that coloration assumption, and is simply defined by joint probability density function (pdf) of successive samples of the sources. The method shows that performance in separation quality is enhanced using this prior, for separation in linear as well as non linear mixtures. The counterpart is an increase of the computation complexity, due to estimation of multivariate pdf estimations.

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