WAVELETS TAILORED TO FUNCTIONAL IMAGING: APPLICATIONS TO FMRI AND DYNAMIC PET

Traditional wavelets have a number of vanishing moments that corresponds to their equivalent order of the derivation. They oer good energy compaction for piecewise smooth signals, but are less appropriate for more complex signals such as those origi-nating in functional imaging; e.g., the hemodynamic response after brain activation in functional magnetic resonance imaging (fMRI) and time activity curves (TACs) in positron emission tomography (PET). The framework of exponential-spline wa-velets [1] allows us to design new wavelet bases that act like a given dierential operator; i.e., they can be tuned to the characteristics of a system and yield a sparse representation of some corresponding class of signals. We show two examples. For fMRI, the wavelets are tuned according to the hemody-namic response of the system. The combination with a ℓ1-regularization constraint reveals brain activation patterns without the knowledge of a stimulation para-digm [2]. For dynamic PET, the wavelets are tailored to the compartmental des-cription of the dynamics of the tracer distribution. The ℓ1-regularization constrain