Deep learning-based MRI reconstruction with Artificial Fourier Transform Network (AFTNet)

Deep complex-valued neural networks (CVNNs) provide a powerful way to leverage complex number operations and representations and have succeeded in several phase-based applications. However, previous networks have not fully explored the impact of complex-valued networks in the frequency domain. Here, we introduce a unified complex-valued deep learning framework - Artificial Fourier Transform Network (AFTNet) - which combines domain-manifold learning and CVNNs. AFTNet can be readily used to solve image inverse problems in domain transformation, especially for accelerated magnetic resonance imaging (MRI) reconstruction and other applications. While conventional methods typically utilize magnitude images or treat the real and imaginary components of k-space data as separate channels, our approach directly processes raw k-space data in the frequency domain, utilizing complex-valued operations. This allows for a mapping between the frequency (k-space) and image domain to be determined through cross-domain learning. We show that AFTNet achieves superior accelerated MRI reconstruction compared to existing approaches. Furthermore, our approach can be applied to various tasks, such as denoised magnetic resonance spectroscopy (MRS) reconstruction and datasets with various contrasts. The AFTNet presented here is a valuable preprocessing component for different preclinical studies and provides an innovative alternative for solving inverse problems in imaging and spectroscopy. The code is available at: https://github.com/yanting-yang/AFT-Net.