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Partial scan is a common approach to accelerate Magnetic Resonance Imaging(MRI) data acquisition in both 2D and 3D settings. However, accuratelyreconstructing images from partial scan data (i.e., incomplete k-spacematrices) remains challenging due to lack of an effectively global receptivefield in both spatial and k-space domains. To address this problem, we proposethe following: (1) a novel convolutional operator called Faster FourierConvolution (FasterFC) to replace the two consecutive convolution operationstypically used in convolutional neural networks (e.g., U-Net, ResNet). Based onthe spectral convolution theorem in Fourier theory, FasterFC employsalternating kernels of size 1 in 3D case) in different domains to extend thedual-domain receptive field to the global and achieves faster calculation speedthan traditional Fast Fourier Convolution (FFC). (2) A 2D accelerated MRImethod, FasterFC-End-to-End-VarNet, which uses FasterFC to improve thesensitivity maps and reconstruction quality. (3) A multi-stage 3D acceleratedMRI method called FasterFC-based Single-to-group Network (FAS-Net) thatutilizes a single-to-group algorithm to guide k-space domain reconstruction,followed by FasterFC-based cascaded convolutional neural networks to expand theeffective receptive field in the dual-domain. Experimental results on thefastMRI and Stanford MRI Data datasets demonstrate that FasterFC improves thequality of both 2D and 3D reconstruction. Moreover, FAS-Net, as a 3Dhigh-resolution multi-coil (eight) accelerated MRI method, achieves superiorreconstruction performance in both qualitative and quantitative resultscompared with state-of-the-art 2D and 3D methods.

Image Reconstruction for Accelerated MR Scan with Faster Fourier Convolutional Neural Networks