Abstract
In this paper, we present a novel variational formulation for restoring high angular resolution diffusion imaging (HARDI) data. The restoration formulation involves smoothing signal measurements over the spherical domain and across the 3D image lattice. The regularization across the lattice is achieved using a total variation (TV) norm based scheme, while the finite element method (FEM) was employed to smooth the data on the sphere at each lattice point using first and second order smoothness constraints. Examples are presented to show the performance of the HARDI data restoration scheme and its effect on fiber direction computation on synthetic data, as well as on real data sets collected from excised rat brain and spinal cord.
Highlights
Observing the directional dependence of water diffusion in the nervous system can allow us to infer structural information about the surround ing tissue
The rest of this paper is organized as follows: Section (2) contains a variational formulation of the high angular resolution diffusion imaging (HARDI) denoising problem including smoothing the scalar signal over a sphere of directions at each 3D lattice point and across lattice points, com putation of probability of water molecular diffusion over the sphere of directions and several measures of anisotropy computed from the field of probability densities
We present a variational formulation for effective denoising of the HARDI data
Summary
Observing the directional dependence of water diffusion in the nervous system can allow us to infer structural information about the surround ing tissue. The use of spherical harmonic expansions have been quite popular in this context since the HARDI data primarily consists of scalar signal measurements on a sphere located at each lattice point on a 3D image grid. Their analytic form for the ODF reconstruction requires a numerical solution to a linear system and they do not consider regularization across the 3D lattice which can be important in order to obtain a piecewise smooth repre sentation of the given HARDI data.
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