Diffusion tensor imaging (DTI) MRI is a noninvasive imaging method of the cerebral tissues whose fibers directions are not evaluated correctly in the regions of the crossing fibers. For the same reason the high angular resolution diffusion images (HARDI) are used for estimation of the fiber direction in each voxel. One of the main methods to specify the direction of fibers is usage of the spher...

This paper proposes nonparametric deconvolution density estimation over S 2. Here we would think of the S 2 elements of interest being corrupted by random SO(3) elements (rotations). The resulting density on the observations would be a convolution of the SO(3) density with the true S 2 density. Consequently, the methodology, as in the Euclidean case, would be to use Fourier analysis on SO(3) an...

This paper addresses the issue of optimal deconvolution density estimation on the 2-sphere. Indeed, by using the transitive group action of the rotation matrices on the 2-dimensional unit sphere, rotational errors can be introduced analogous to the Euclidean case. The resulting density turns out to be convolution in the Lie group sense and so the statistical problem is to recover the true under...

Introduction:. Standard spherical deconvolution approaches assume that HARDI signal can be modeled as a convolution between a common fiber response and a fiber orientation distribution function [1][2]. Recent spherical deconvolution methods improved the quality of the results introducing the non negative constraint of the solution [3][4][5]. It can be verified, however, that instability problem...

BACKGROUND AND PURPOSE MR imaging tractography is increasingly used to perform noninvasive presurgical planning for brain gliomas. Recently, constrained spherical deconvolution tractography was shown to overcome several limitations of commonly used DTI tractography. The purpose of our study was to evaluate WM tract alterations of both the corticospinal tract and arcuate fasciculus in patients w...

Diffusion-weighted MRI has enabled the imaging of white matter architecture in vivo. Fiber orientations have classically been assumed to lie along the major eigenvector of the diffusion tensor, but this approach has well-characterized shortcomings in voxels containing multiple fiber populations. Recently proposed methods for recovery of fiber orientation via spherical deconvolution utilize a sp...