  Cardiac magnetic resonance imaging (MRI) requires reconstructing a real-time
video of a beating heart from continuous highly under-sampled measurements.
This task is challenging since the object to be reconstructed (the heart) is
continuously changing during signal acquisition. In this paper, we propose a
reconstruction approach based on representing the beating heart with an
implicit neural network and fitting the network so that the representation of
the heart is consistent with the measurements. The network in the form of a
multi-layer perceptron with Fourier-feature inputs acts as an effective signal
prior and enables adjusting the regularization strength in both the spatial and
temporal dimensions of the signal. We study the proposed approach for 2D
free-breathing cardiac real-time MRI in different operating regimes, i.e., for
different image resolutions, slice thicknesses, and acquisition lengths. Our
method achieves reconstruction quality on par with or slightly better than
state-of-the-art untrained convolutional neural networks and superior image
quality compared to a recent method that fits an implicit representation
directly to Fourier-domain measurements. However, this comes at a relatively
high computational cost. Our approach does not require any additional patient
data or biosensors including electrocardiography, making it potentially
applicable in a wide range of clinical scenarios.
