  We propose a novel unsupervised deep-learning-based algorithm for dynamic
magnetic resonance imaging (MRI) reconstruction. Dynamic MRI requires rapid
data acquisition for the study of moving organs such as the heart. Existing
reconstruction methods suffer from restrictions either in the model design or
in the absence of ground-truth data, resulting in low image quality. We
introduce a generalized version of the deep-image-prior approach, which
optimizes the network weights to fit a sequence of sparsely acquired dynamic
MRI measurements. Our method needs neither prior training nor additional data.
In particular, for cardiac images, it does not require the marking of
heartbeats or the reordering of spokes. The key ingredients of our method are
threefold: 1) a fixed low-dimensional manifold that encodes the temporal
variations of images; 2) a network that maps the manifold into a more
expressive latent space; and 3) a convolutional neural network that generates a
dynamic series of MRI images from the latent variables and that favors their
consistency with the measurements in k-space. Our method outperforms the
state-of-the-art methods quantitatively and qualitatively in both retrospective
and real fetal cardiac datasets. To the best of our knowledge, this is the
first unsupervised deep-learning-based method that can reconstruct the
continuous variation of dynamic MRI sequences with high spatial resolution.
