  Many neuroimaging studies focus on the cortex, in order to benefit from
better signal to noise ratios and reduced computational burden. Cortical data
are usually projected onto a reference mesh, where subsequent analyses are
carried out. Several multiscale approaches have been proposed for analyzing
these surface data, such as spherical harmonics and graph wavelets. As far as
we know, however, the hierarchical structure of the template icosahedral meshes
used by most neuroimaging software has never been exploited for cortical data
factorization. In this paper, we demonstrate how the structure of the
ubiquitous icosahedral meshes can be exploited by data factorization methods
such as sparse dictionary learning, and we assess the optimization speed-up
offered by extrapolation methods in this context. By testing different
sparsity-inducing norms, extrapolation methods, and factorization schemes, we
compare the performances of eleven methods for analyzing four datasets: two
structural and two functional MRI datasets obtained by processing the data
publicly available for the hundred unrelated subjects of the Human Connectome
Project. Our results demonstrate that, depending on the level of details
requested, a speedup of several orders of magnitudes can be obtained.
