  Motion degradation is a central problem in Magnetic Resonance Imaging (MRI).
This work addresses the problem of how to obtain higher quality, super-resolved
motion-free, reconstructions from highly undersampled MRI data. In this work,
we present for the first time a variational multi-task framework that allows
joining three relevant tasks in MRI: reconstruction, registration and
super-resolution. Our framework takes a set of multiple undersampled MR
acquisitions corrupted by motion into a novel multi-task optimisation model,
which is composed of an $L^2$ fidelity term that allows sharing representation
between tasks, super-resolution foundations and hyperelastic deformations to
model biological tissue behaviors. We demonstrate that this combination yields
to significant improvements over sequential models and other bi-task methods.
Our results exhibit fine details and compensate for motion producing sharp and
highly textured images compared to state of the art methods.
