  We present a rotation-equivariant unsupervised learning framework for the
sparse deconvolution of non-negative scalar fields defined on the unit sphere.
Spherical signals with multiple peaks naturally arise in Diffusion MRI (dMRI),
where each voxel consists of one or more signal sources corresponding to
anisotropic tissue structure such as white matter. Due to spatial and spectral
partial voluming, clinically-feasible dMRI struggles to resolve crossing-fiber
white matter configurations, leading to extensive development in spherical
deconvolution methodology to recover underlying fiber directions. However,
these methods are typically linear and struggle with small crossing-angles and
partial volume fraction estimation. In this work, we improve on current
methodologies by nonlinearly estimating fiber structures via unsupervised
spherical convolutional networks with guaranteed equivariance to spherical
rotation. Experimentally, we first validate our proposition via extensive
single and multi-shell synthetic benchmarks demonstrating competitive
performance against common baselines. We then show improved downstream
performance on fiber tractography measures on the Tractometer benchmark
dataset. Finally, we show downstream improvements in terms of tractography and
partial volume estimation on a multi-shell dataset of human subjects.
