Analysis of event-related fMRI data using best clustering bases

We explore a new paradigm for the analysis of event-related functional magnetic resonance images (fMRI) of brain activity. We regard the fMRI data as a very large set of time series x_i(t), indexed by the position i of a voxel inside the brain. The decision that a voxel i₀ is activated is based not solely on the value of the fMRI signal at i₀, but rather on the comparison of all time series x_i(t) in a small neighborhood W_i(0) around i₀. We construct basis functions on which the projection of the fMRI data reveals the organization of the time series x_i(t) into activated and nonactivated clusters. These clustering basis functions are selected from large libraries of wavelet packets according to their ability to separate the fMRI time series into the activated cluster and a nonactivated cluster. This principle exploits the intrinsic spatial correlation that is present in the data. The construction of the clustering basis functions described in this paper is applicable to a large category of problems where time series are indexed by a spatial variable.