  Partial scan is a common approach to accelerate Magnetic Resonance Imaging
(MRI) data acquisition in both 2D and 3D settings. However, accurately
reconstructing images from partial scan data (i.e., incomplete k-space
matrices) remains challenging due to lack of an effectively global receptive
field in both spatial and k-space domains. To address this problem, we propose
the following: (1) a novel convolutional operator called Faster Fourier
Convolution (FasterFC) to replace the two consecutive convolution operations
typically used in convolutional neural networks (e.g., U-Net, ResNet). Based on
the spectral convolution theorem in Fourier theory, FasterFC employs
alternating kernels of size 1 in 3D case) in different domains to extend the
dual-domain receptive field to the global and achieves faster calculation speed
than traditional Fast Fourier Convolution (FFC). (2) A 2D accelerated MRI
method, FasterFC-End-to-End-VarNet, which uses FasterFC to improve the
sensitivity maps and reconstruction quality. (3) A multi-stage 3D accelerated
MRI method called FasterFC-based Single-to-group Network (FAS-Net) that
utilizes a single-to-group algorithm to guide k-space domain reconstruction,
followed by FasterFC-based cascaded convolutional neural networks to expand the
effective receptive field in the dual-domain. Experimental results on the
fastMRI and Stanford MRI Data datasets demonstrate that FasterFC improves the
quality of both 2D and 3D reconstruction. Moreover, FAS-Net, as a 3D
high-resolution multi-coil (eight) accelerated MRI method, achieves superior
reconstruction performance in both qualitative and quantitative results
compared with state-of-the-art 2D and 3D methods.
