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Cardiac magnetic resonance imaging (MRI) requires reconstructing a real-timevideo of a beating heart from continuous highly under-sampled measurements.This task is challenging since the object to be reconstructed (the heart) iscontinuously changing during signal acquisition. In this paper, we propose areconstruction approach based on representing the beating heart with animplicit neural network and fitting the network so that the representation ofthe heart is consistent with the measurements. The network in the form of amulti-layer perceptron with Fourier-feature inputs acts as an effective signalprior and enables adjusting the regularization strength in both the spatial andtemporal dimensions of the signal. We study the proposed approach for 2Dfree-breathing cardiac real-time MRI in different operating regimes, i.e., fordifferent image resolutions, slice thicknesses, and acquisition lengths. Ourmethod achieves reconstruction quality on par with or slightly better thanstate-of-the-art untrained convolutional neural networks and superior imagequality compared to a recent method that fits an implicit representationdirectly to Fourier-domain measurements. However, this comes at a relativelyhigh computational cost. Our approach does not require any additional patientdata or biosensors including electrocardiography, making it potentiallyapplicable in a wide range of clinical scenarios.

Implicit Neural Networks with Fourier-Feature Inputs for Free-breathing Cardiac MRI Reconstruction