Analysis of fMRI Data Using Spline Wavelets

Our goal is to detect and localize areas of activation in the brain from sequences of fMRI images. The standard approach for reducing the noise contained in the fMRI images is to apply a spatial Gaussian filter which entails some loss of details. Here instead, we consider a wavelet solution to the problem, which has the advantage of retaining high-frequency information. We use fractional-spline orthogonal wavelets with a continuously-varying order parameter alpha; by adjusting alpha, we can balance spatial resolution against frequency localization. The activation pattern is detected by performing multiple (Bonferroni-corrected) t-tests in the wavelet domain. This pattern is then localized by inverse wavelet transform of a thresholded coefficient map. In order to compare transforms and to select the best alpha, we devise a simulation study for the detection of a known activation pattern. We also apply our methodology to the analysis of acquired fMRI data for a motor task