  In fully sampled cardiac MR (CMR) acquisitions, motion can lead to corruption
of k-space lines, which can result in artefacts in the reconstructed images. In
this paper, we propose a method to automatically detect and correct
motion-related artefacts in CMR acquisitions during reconstruction from k-space
data. Our correction method is inspired by work on undersampled CMR
reconstruction, and uses deep learning to optimize a data-consistency term for
under-sampled k-space reconstruction. Our main methodological contribution is
the addition of a detection network to classify motion-corrupted k-space lines
to convert the problem of artefact correction to a problem of reconstruction
using the data consistency term. We train our network to automatically correct
for motion-related artefacts using synthetically corrupted cine CMR k-space
data as well as uncorrupted CMR images. Using a test set of 50 2D+time cine CMR
datasets from the UK Biobank, we achieve good image quality in the presence of
synthetic motion artefacts. We quantitatively compare our method with a variety
of techniques for recovering good image quality and showcase better performance
compared to state of the art denoising techniques with a PSNR of 37.1.
Moreover, we show that our method preserves the quality of uncorrupted images
and therefore can be also utilized as a general image reconstruction algorithm.
