The inductive bias of the convolutional neural network (CNN) can be a strong prior for image restoration, which is known as the Deep Image Prior (DIP). Recently, DIP is utilized in unsupervised dynamic MRI reconstruction, which adopts a generative model from the latent space to the image space. However, existing methods usually use a pyramid-shaped CNN generator shared by all frames, embedding the temporal modeling within the latent space, which may hamper the model expression capability. In this work, we propose a novel scheme for dynamic MRI representation, named ``Graph Image Prior'' (GIP). GIP adopts a two-stage generative network in a new modeling methodology, which first employs independent CNNs to recover the image structure for each frame, and then exploits the spatio-temporal correlations within the feature space parameterized by a graph model. A graph convolutional network is utilized for feature fusion and dynamic image generation. In addition, we devise an ADMM algorithm to alternately optimize the images and the network parameters to improve the reconstruction performance. Experiments were conducted on cardiac cine MRI reconstruction, which demonstrate that GIP outperforms compressed sensing methods and other DIP-based unsupervised methods, significantly reducing the performance gap with state-of-the-art supervised algorithms. Moreover, GIP displays superior generalization ability when transferred to a different reconstruction setting, without the need for any additional data.

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