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Start of funding 01.07.2005

Sparse constrained signal decomposition - theory and application to biomedical data analysis

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Model-free, blind signal decomposition of observed multivariate data sets has important applications in biomedical data analysis like EEGLAB co-developed by Dr. Lee at SALK. Our project joins the experience of the Californian group in underdetermined and convolved source separation with the theoretical knowledge in constrained and sparse matrix factorization algorithms of the Bavarian partner accumulated within the project ModKog. We propose a new approach to biomedical data analysis based on sparseness of the involved signals together with additional model constraints. The latter mirror known facts of biomedical data sets and allow for a flexible analysis.

Final report:
Model-free identification of brain activity in functional MRI data

In this contribution, a factorization model to decompose multivariate data sets is reviewed, both in theory and applications. The interplay of novel modeling results and corresponding algorithms with applications is illustrated human brain recordings from functional magnetic resonance imaging (fMRI).

Second-order source separation and multidimensional generalizations

Blind Source Separation (BSS) describes the problem of identifying hidden unknown source signals within a multivariate observed mixture. SOBI is a blind source separation algorithm based on the assumption of time decorrelated source signals. In imaging data sets, in particular in fMRI data, not only two- but also three-dimensional autocorrelations are available. Hence, we have developed an extension called mdSOBI by using multidimensional autocovariances, which can be efficiently calculated for data sets with multidimensional parameterizations. mdSOBI has the advantage of using the spatial data in all directions, whereas SOBI only uses a single direction. These findings are confirmed by simulations and applications to fMRI analysis, where mdSOBI outperforms SOBI considerably.

Spatiotemporal BSS

Commonly, temporal Blind Source Separation (BSS) is performed to separate data sets. However, if the data possesses both spatial and temporal structures, such as fMRI scans, we can require the transformed data to be as independent as possible in both dimensions.

First introduced by Stone et al, spatiotemporal BSS is a promising method for fMRI data analysis. We propose two novel algorithms for performing spatiotemporal BSS by jointly diagonalizing different quantities of the mixtures, both in time and in space.

The generalization of ICA (Independent Component Analysis), namely the JADE algorithm, is realized by spatiotemporal JADE (stJADE), which uses double-sided joint diagonalization of fourth-order cumulants. Similarly, we generalize the SOBI algorithm with spatiotemporal SOBI (stSOBI) by performing double-sided joint diagonalization of time / spatially delayed autocovariances.