High dimensional spatiotemporal datasets are routinely acquired in many areas of biology and medicine. These datasets have a particular structure: they are composed of temporal signals that are indexed by their position. A time series of functional Magnetic Resonance Images (fMRI) is an example of such datasets. FMRI can quantify hemodynamic changes induced by neuronal activity when a subject is submitted to sensory or cognitive stimulations. The goal of the analysis is to detect the "activated" voxels where the changes in the fMRI signal can be considered to be triggered by the stimulus.
The goal of this work is to show that one can find interesting projections of the fMRI signal that reveal the presence of activated time series. These projections are selected from large libraries of wavelet packets by studying the probability distribution of the wavelet packet coefficients. We model this distribution with a finite mixture of multivariate Gaussian densities. We develop methods for estimating the number of components in the mixture, their associated parameters, and interpret their physiological roles.
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