Wavelet smoothing of fMRI activation images
Images from functional imaging experiments are subject to a data processing stream involving motion correction and spatial normalization. The next step is then to smooth the images using a Gaussian kernel. One reason for the smoothing step is to render activation information amenable to classical statistical inference via Random Field Theory. This requires that the residual fields have a smoothness, measured by the Full Width at Half Maximum (FWHM) of a Gaussian kernel, that is of the order of three times the voxel edge size. If one were to abandon the classical inference framework in favour of Bayesian inference however, see eg. [5], then the above motivation for smoothing disappears. This then leaves the second reason for smoothing which derives from the fact that a point mass of neural activity gives rise to a spatially extended hemodynamic response, the relation being defined by the spatial hemodynamic Point Response Function (PRF). If one assumes that the PRF is Gaussian with a known FWHM, then one can increase the Signal-to-Noise Ratio (SNR) in functional images by smoothing with that kernel. Overor under specification of the FWHM, however, will lead to suboptimal increase in SNR. Further, if the PRF is non-stationary then smoothing with a fixed size Gaussian kernel is clearly sub-optimal. This provides the motivation for smoothing with other methods such as wavelets.