Euclidian distance-weighted smoothing for quantitative MRI: application to intervoxel anisotropy index mapping with DTI

During the computation of intervoxel anisotropy features, the inclusion of both eigenvalues and eigenvectors reduces the effect of noise, but spatial averaging blurs the resulting maps. We propose a new adaptive technique that uses data-dependent weights in the averaging process so that the influence of each neighbor in the local window is proportional to the similarity of characteristics of the neighbor considered to those of the reference central voxel. This likeness criterion is based on the multidimensional Euclidian distance using the entire available multispectral information contained in the diffusion-weighted images. This solution is controlled by a single parameter beta that results from a compromise between edge-preserving and noise-smoothing abilities. This Euclidian distance-weighted technique is a generic solution for filtering noise during parametric reconstruction. It was applied to map anisotropy using an intervoxel lattice index (LI) from experimental images of mouse brain in vivo and achieves noise reduction without distorting small anatomical structures. We also show how to employ in the discrimination scheme the images not used in the estimation of the considered feature.