Deep Learning-based MRI Reconstruction with Artificial Fourier Transform (AFT)-Net

The deep complex-valued neural network provides a powerful way to leverage complex number operations and representations, which has succeeded in several phase-based applications. However, most previously published networks have not fully accessed the impact of complex-valued networks in the frequency domain. Here, we introduced a unified complex-valued deep learning framework - artificial Fourier transform network (AFT-Net) - which combined domain-manifold learning and complex-valued neural networks. The AFT-Net can be readily used to solve the image inverse problems in domain-transform, especially for accelerated magnetic resonance imaging (MRI) reconstruction and other applications. While conventional methods only accept magnitude images, the proposed method takes raw k-space data in the frequency domain as inputs, allowing a mapping between the k-space domain and the image domain to be determined through cross-domain learning. We show that AFT-Net achieves superior accelerated MRI reconstruction and is comparable to existing approaches. Also, our approach can be applied to different tasks like denoised MRS reconstruction and different datasets with various contrasts. The AFT-Net presented here is a valuable preprocessing component for different preclinical studies and provides an innovative alternative for solving inverse problems in imaging and spectroscopy.