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.

翻译：局部扫描是加速二维和三维磁共振成像（MRI）数据采集的常用方法。然而，由于在空间域和k空间域均缺乏有效的全局感受野，从局部扫描数据（即不完整的k空间矩阵）中精确重建图像仍具挑战。为解决此问题，我们提出以下方法：（1）一种新型卷积算子——更快傅里叶卷积（FasterFC），用于替代卷积神经网络（如U-Net、ResNet）中常用的连续两次卷积操作。基于傅里叶理论中的谱卷积定理，FasterFC在不同域中交替使用大小为1（三维情形下）的卷积核，将双域感受野扩展至全局，且计算速度优于传统快速傅里叶卷积（FFC）。（2）一种二维加速MRI方法FasterFC-End-to-End-VarNet，通过FasterFC提升灵敏度图与重建质量。（3）一种多阶段三维加速MRI方法——基于FasterFC的单到组网络（FAS-Net），该方法利用单到组算法引导k空间域重建，随后通过基于FasterFC的级联卷积神经网络扩展双域有效感受野。在fastMRI与Stanford MRI Data数据集上的实验结果表明，FasterFC提升了二维与三维重建质量。此外，作为三维高分辨率多线圈（八通道）加速MRI方法，FAS-Net在定性与定量结果上均优于当前最先进的二维与三维方法，实现了卓越的重建性能。