  Deep learning models have been widely applied for fast MRI. The majority of
existing deep learning models, e.g., convolutional neural networks, work on
data with Euclidean or regular grids structures. However, high-dimensional
features extracted from MR data could be encapsulated in non-Euclidean
manifolds. This disparity between the go-to assumption of existing models and
data requirements limits the flexibility to capture irregular anatomical
features in MR data. In this work, we introduce a novel Vision GNN type network
for fast MRI called Vision GNN U-Net (ViGU). More precisely, the pixel array is
first embedded into patches and then converted into a graph. Secondly, a
U-shape network is developed using several graph blocks in symmetrical encoder
and decoder paths. Moreover, we show that the proposed ViGU can also benefit
from Generative Adversarial Networks yielding to its variant ViGU-GAN. We
demonstrate, through numerical and visual experiments, that the proposed ViGU
and GAN variant outperform existing CNN and GAN-based methods. Moreover, we
show that the proposed network readily competes with approaches based on
Transformers while requiring a fraction of the computational cost. More
importantly, the graph structure of the network reveals how the network
extracts features from MR images, providing intuitive explainability.
