We present a novel method for higher order reconstruction
of fetal diffusion MRI signal that enables detection of
fiber crossings. We combine data-driven motion and intensity
correction with super-resolution reconstruction and spherical
harmonic parametrisation to reconstruct data scattered in both
spatial and angular domains into consistent fetal dMRI signal
suitable for further diffusion analysis. We show that intensity
correction is essential for good performance of the method and
identify anatomically plausible fiber crossings. The proposed
methodology has potential to facilitate detailed investigation of
developing brain connectivity and microstructure in-utero.