Deep Learning-based MRI Reconstruction with Artificial Fourier Transform Network (AFTNet)

TL;DR

This work targets inverse problems in MRI by addressing undersampling artifacts through cross-domain learning between $k$-space and image domains. It introduces the Artificial Fourier Transform (AFT) block, a learnable alternative to the discrete Fourier transform, which is embedded into complex-valued networks to form AFTNet. The approach demonstrates competitive, and often superior, performance for 2D MRI reconstruction, accelerated MRI, and 1D MRS denoising, validating the benefits of processing complex-valued data directly in the frequency domain. By enabling a modular, generalizable framework that jointly leverages frequency-domain and image-domain features, the method offers a practical, robust preprocessing component for diverse imaging and spectroscopy inverse problems.

Abstract

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.

Figures (10)

• Figure 1: Schematics of general deep-learning MR imaging/spectroscopy reconstruction based on AFTNet. The inputs of AFTNet can be 2D MRI k-space data or 1D MRS FID data. The outputs are reconstructed MR images or spectra. Different structures of AFTNet are developed by appending front-end and/or back-end convolutional networks to the AFT block. Here we show the T2w 1.5T MRI and 3T PRESS MRS reconstruction results, respectively. C: complex-valued and R: real-valued.
• Figure 1: 1D 4x equal-spaced sampling mask with 8% of low-frequency columns retained. While space indicates the signal retained and black space indicates the signal masked out.
• Figure 2: Structure of 2-dimensional AFTNet. Components include the complex-valued AFT block, the complex-valued residual attention UNet, the complex-valued residual block, and the complex-valued attention gate. All convolutional layers have a kernel size of 3, except those pointed out specifically. C: complex-valued. Red numbers indicate the number of channels produced by each layer.
• Figure 3: The workflows of experiments on each dataset.
• Figure 4: Comparison between baseline methods and AFTNet. Here we present the qualitative results f a T2w image on 3T