Dual-domain faster Fourier convolution based network for MR image reconstruction

Deep learning methods for fast MRI have shown promise in reconstructing high-quality images from undersampled multi-coil k-space data, leading to reduced scan duration. However, existing methods encounter challenges related to limited receptive fields in dual-domain (k-space and image domains) reconstruction networks, rigid data consistency operations, and suboptimal refinement structures, which collectively restrict overall reconstruction performance. This study introduces a comprehensive framework that addresses these challenges and enhances MR image reconstruction quality. Firstly, we propose Faster Inverse Fourier Convolution (FasterIFC), a frequency domain convolutional operator that significantly expands the receptive field of k-space domain reconstruction networks. Expanding the information extraction range to the entire frequency spectrum according to the spectral convolution theorem in Fourier theory enables the network to easily utilize richer redundant long-range information from adjacent, symmetrical, and diagonal locations of multi-coil k-space data. Secondly, we introduce a novel softer Data Consistency (softerDC) layer, which achieves an enhanced balance between data consistency and smoothness. This layer facilitates the implementation of diverse data consistency strategies across distinct frequency positions, addressing the inflexibility observed in current methods. Finally, we present the Dual-Domain Faster Fourier Convolution Based Network (D2F2), which features a centrosymmetric dual-domain parallel structure based on FasterIFC. This architecture optimally leverages dual-domain data characteristics while substantially expanding the receptive field in both domains. Coupled with the softerDC layer, D2F2 demonstrates superior performance on the NYU fastMRI dataset at multiple acceleration factors, surpassing state-of-the-art methods in both quantitative and qualitative evaluations.