  Motion-resolved reconstruction for abdominal magnetic resonance imaging (MRI)
remains a challenge due to the trade-off between residual motion blurring
caused by discretized motion states and undersampling artefacts. In this work,
we propose to generate blurring-free motion-resolved abdominal reconstructions
by learning a neural implicit representation directly in k-space (NIK). Using
measured sampling points and a data-derived respiratory navigator signal, we
train a network to generate continuous signal values. To aid the regularization
of sparsely sampled regions, we introduce an additional informed correction
layer (ICo), which leverages information from neighboring regions to correct
NIK's prediction. Our proposed generative reconstruction methods, NIK and
ICoNIK, outperform standard motion-resolved reconstruction techniques and
provide a promising solution to address motion artefacts in abdominal MRI.
