  The connectivity and structural integrity of the white matter of the brain is
nowadays known to be implicated into a wide range of brain-related disorders.
However, it was not before the advent of diffusion Magnetic Resonance Imaging
(dMRI) that researches have been able to examine the properties of white matter
in vivo. Presently, among a range of various methods of dMRI, high angular
resolution diffusion imaging (HARDI) is known to excel in its ability to
provide reliable information about the local orientations of neural fasciculi
(aka fibre tracts). Moreover, as opposed to the more traditional diffusion
tensor imaging (DTI), HARDI is capable of distinguishing the orientations of
multiple fibres passing through a given spatial voxel. Unfortunately, the
ability of HARDI to discriminate between neural fibres that cross each other at
acute angles is always limited, which is the main reason behind the development
of numerous post-processing tools, aiming at the improvement of the directional
resolution of HARDI. Among such tools is spherical deconvolution (SD). Due to
its ill-posed nature, however, SD standardly relies on a number of a priori
assumptions which are to render its results unique and stable. In this paper,
we propose a different approach to the problem of SD in HARDI, which accounts
for the spatial continuity of neural fibres as well as the presence of
isotropic diffusion. Subsequently, we demonstrate how the proposed solution can
be used to successfully overcome the effect of partial voluming, while
preserving the spatial coherency of cerebral diffusion at moderate-to-severe
noise levels. In a series of both in silico and in vivo experiments, the
performance of the proposed method is compared with that of several available
alternatives, with the comparative results clearly supporting the viability and
usefulness of our approach.
