  In the last decade diffusion MRI has become a powerful tool to non-invasively
study white-matter integrity in the brain. Recently many research groups have
focused their attention on multi-shell spherical acquisitions with the aim of
effectively mapping the diffusion signal with a lower number of q-space
samples, hence enabling a crucial reduction of acquisition time. One of the
quantities commonly studied in this context is the so-called orientation
distribution function (ODF). In this setting, the spherical harmonic (SH)
transform has gained a great deal of popularity thanks to its ability to
perform convolution operations efficiently and accurately, such as the
Funk-Radon transform notably required for ODF computation from q-space data.
However, if the q-space signal is described with an unsuitable angular
resolution at any b-value probed, aliasing (or interpolation) artifacts are
unavoidably created. So far this aspect has been tackled empirically and, to
our knowledge, no study has addressed this problem in a quantitative approach.
The aim of the present work is to study more theoretically the efficiency of
multi-shell spherical sampling in diffusion MRI, in order to gain understanding
in HYDI-like approaches, possibly paving the way to further optimization
strategies.
