  MRI, a widespread non-invasive medical imaging modality, is highly sensitive
to patient motion. Despite many attempts over the years, motion correction
remains a difficult problem and there is no general method applicable to all
situations. We propose a retrospective method for motion estimation and
correction to tackle the problem of in-plane rigid-body motion, apt for
classical 2D Spin-Echo scans of the brain, which are regularly used in clinical
practice. Due to the sequential acquisition of k-space, motion artifacts are
well localized. The method leverages the power of deep neural networks to
estimate motion parameters in k-space and uses a model-based approach to
restore degraded images to avoid ''hallucinations''. Notable advantages are its
ability to estimate motion occurring in high spatial frequencies without the
need of a motion-free reference. The proposed method operates on the whole
k-space dynamic range and is moderately affected by the lower SNR of higher
harmonics. As a proof of concept, we provide models trained using supervised
learning on 600k motion simulations based on motion-free scans of 43 different
subjects. Generalization performance was tested with simulations as well as
in-vivo. Qualitative and quantitative evaluations are presented for motion
parameter estimations and image reconstruction. Experimental results show that
our approach is able to obtain good generalization performance on simulated
data and in-vivo acquisitions. We provide a Python implementation at
https://gitlab.unige.ch/Oscar.Dabrowski/sismik_mri/.
