  Brain activation mapping using functional MRI (fMRI) based on blood
oxygenation level-dependent (BOLD) contrast has been conventionally focused on
probing gray matter, the BOLD contrast in white matter having been generally
disregarded. Recent results have provided evidence of the functional
significance of the white matter BOLD signal, showing at the same time that its
correlation structure is highly anisotropic, and related to the diffusion
tensor in shape and orientation. This evidence suggests that conventional
isotropic Gaussian filters are inadequate for denoising white matter fMRI data,
since they are incapable of adapting to the complex anisotropic domain of white
matter axonal connections. In this paper we explore a graph-based description
of the white matter developed from diffusion MRI data, which is capable of
encoding the anisotropy of the domain. Based on this representation we design
localized spatial filters that adapt to white matter structure by leveraging
graph signal processing principles. The performance of the proposed filtering
technique is evaluated on semi-synthetic data, where it shows potential for
greater sensitivity and specificity in white matter activation mapping,
compared to isotropic filtering.
