Robust anisotropic diffusion to produce enhanced statistical parametric map from noisy fMRI

This paper presents a new, simple, and elegant technique to obtain enhanced statistical parametric maps (SPMs) from noisy functional magnetic resonance imaging (fMRI) data. This technique is based on the robust anisotropic diffusion (RAD), a technique normally used as an edge-preserving filter. A direct application of the RAD to the fMRI data does not work, because in this case RAD would perform an edge-preserving filtering of the fMRI structural information, instead of enhancing its functional information. The RAD can be applied directly to SPM but, in this case, only a small improvement of the SPM quality can be achieved, because the originating fMRI is not taken into account. To overcome these difficulties, we propose to estimate the SPM from the noisy fMRI, compute the diffusion coefficients in the SPM space, and then perform the diffusion in the structural information-removed fMRI data using the coefficients previously computed. These steps are iterated until convergence. We have tested the new technique in both simulated and real fMRI images, yielding surprisingly sharp and noiseless SPMs with increased statistical significance. We also describe how to automatically estimate an appropriate scale parameter.