Wavelet-Based Statistical Analysis in Functional Neuroimaging

Wavelet-based analysis versus Gaussian smoothing in statistical parametric mapping (SPM) for detecting and analyzing brain activity from functional magnetic resonance imaging (fMRI) data is presented. Detection of activation in fMRI data can be performed in the wavelet domain by a coefficient-wise statistical t-test. The link between the wavelet analysis and SPM is based on two observations: (i) the low-pass analysis filter of the discrete wavelet transform (DWT) can be similarly shaped to a Gaussian filter in SPM, (ii) the subsampling scheme provides means to define the number of coefficients in the low-pass subband of the wavelet decomposition [52]. Analysis of an fMRI block-based visual stimulation paradigm was comparatively performed by wavelet analysis and statistical parametric mapping (SPM) [13] based on the Random Field Theory (RFT). The voxels were isotropic and the same general linear model (GLM) was employed in both the image space and the wavelet domain. Consequently, an equivalent spline degree for which the low-pass part of the wavelet analysis is basically equivalent to SPM can be computed. The processing of neuroimaging data in the wavelet domain was carried out by means of two different biorthogonal transforms: 3D fractional-spline wavelets and 2D+Z fractional quincunx wavelets [51], resulting in activation patterns similar to the activation maps obtained by linear regression analysis in SPM. Key–Words: Wavelets, Fourier transform, multiresolution analysis, functional magnetic resonance imaging, general linear model, statistical parametric mapping.