  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.
