Decomposition of fMRI data into multiple components

The goal of this work is to provide a new representation of functional magnetic resonance imaging (fMRI) time series. Functional neuroimaging aims at quantifying and localizing neuronal activity using imaging techniques. Functional MRI can detect and quantify hemodynamic changes induced by brain activation and neuronal activity. The time course of the fMRI signal at a given voxel inside the brain is represented with a structural model where each component of the model belongs to a subspace spanned by a small number of basis functions. The basis functions in different subspaces have very distinct time-frequency characteristics. The large scale trend of the signal is represented with a combination of large scale wavelets. The response to the stimulus is expanded on a small set of basis functions, Because it is critical to adapt the basis functions to the type of stimulus, the evoked response to a random presentation is expanded into small scale wavelets or wavelet packets, while the response to a periodic stimulus is represented with cosine or sine functions. We illustrate the estimation of the components of the model with several experiments.