Spherical Deconvolution

Spherical Deconvolution

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...

Localized spherical deconvolution

Optimal Spherical Deconvolution

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...

The dictionary approach for spherical deconvolution

We consider the problem of estimating a density of probability from indirect data in the spherical convolution model. We aim at building an estimate of the unknown density as a linear combination of functions of an overcomplete dictionary. The procedure is devised through a well-calibrated `1-penalized criterion. The spherical deconvolution setting has been barely studied so far, and the two ma...

Auto-calibrating Spherical Deconvolution Based on ODF Sparsity

Spherical deconvolution models the diffusion MRI signal as the convolution of a fiber orientation density function (fODF) with a single fiber response. We propose a novel calibration procedure that automatically determines this fiber response. This has three advantages: First, the user no longer needs to provide an estimate of the response. Second, we estimate a per-voxel fiber response, which ...