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

High quality image reconstruction from undersampled ${k}$ -space data is key to accelerating MR scanning. Current deep learning methods are limited by the small receptive fields in reconstruction networks, which restrict the exploitation of long-range information, and impede the mitigation of full-image artifacts, particularly in 3D reconstruction tasks. Additionally, the substantial computational demands of 3D reconstruction considerably hinder advancements in related fields. To tackle these challenges, we propose the following: 1) A novel convolution operator named Faster Fourier Convolution (FasterFC), aims at providing an adaptable broad receptive field for spatial domain reconstruction networks with fast computational speed. 2) A split-slice strategy that substantially reduces the computational load of 3D reconstruction, enabling high-resolution, multi-coil, 3D MR image reconstruction while fully utilizing inter-layer and intra-layer information. 3) A single-to-group algorithm that efficiently utilizes scan-specific and data-driven priors to enhance ${k}$ -space interpolation effects. 4) A multi-stage, multi-coil, 3D fast MRI method, called the faster Fourier convolution based single-to-group network (FAS-Net), comprising a single-to-group ${k}$ -space interpolation algorithm and a FasterFC-based image domain reconstruction module, significantly minimizes the computational demands of 3D reconstruction through split-slice strategy. Experimental evaluations conducted on the NYU fastMRI and Stanford MRI Data datasets reveal that the FasterFC significantly enhances the quality of both 2D and 3D reconstruction results. Moreover, FAS-Net, characterized as a method that can achieve high-resolution (320, 320, 256), multi-coil, (8 coils), 3D fast MRI, exhibits superior reconstruction performance compared to other state-of-the-art 2D and 3D methods.