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.

中文翻译：

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使用更快的傅立叶卷积神经网络进行加速 MR 扫描的图像重建

欠采样的高质量图像重建 ${k}$ -空间数据是加速 MR 扫描的关键。当前的深度学习方法受到重建网络中较小感受野的限制，这限制了远程信息的利用，并阻碍了全图像伪影的减轻，特别是在 3D 重建任务中。此外，3D 重建的大量计算需求极大地阻碍了相关领域的进步。为了应对这些挑战，我们提出以下建议：1）一种名为更快傅立叶卷积（FasterFC）的新型卷积算子，旨在为具有快速计算速度的空间域重建网络提供适应性广泛的感受野。 2）分割切片策略，大大减少了3D重建的计算量，实现高分辨率、多线圈、3D MR图像重建，同时充分利用层间和层内信息。 3）单组算法，有效利用扫描特定和数据驱动的先验来增强 ${k}$ -空间插值效果。 4) 多级、多线圈、3D 快速 MRI 方法，称为基于更快傅里叶卷积的单组网络 (FAS-Net)，包括单组 ${k}$ -空间插值算法和基于 FasterFC 的图像域重建模块，通过分割切片策略显着最小化 3D 重建的计算需求。对纽约大学 fastMRI 和斯坦福 MRI 数据集进行的实验评估表明，FasterFC 显着提高了 2D 和 3D 重建结果的质量。此外，FAS-Net 的特点是可以实现高分辨率（320、320、256）、多线圈（8 个线圈）、3D 快速 MRI，与其他最新技术相比，FAS-Net 表现出卓越的重建性能。艺术 2D 和 3D 方法。