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.