# A Hybrid Frequency-domain/Image-domain Deep Network for Magnetic Resonance Image Reconstruction

arXiv: https://arxiv.org/abs/1810.12473 · HTML: https://mlsanity.com/paper/1810.12473/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Oct 2018.

## Built on by (most cited first, 11 of 11)

- [An Optimal Control Framework for Joint-channel Parallel MRI Reconstruction without Coil Sensitivities](https://mlsanity.com/paper/2109.09738/) (2021)
- [An Interpretable MRI Reconstruction Network with Two-grid-cycle Correction and Geometric Prior Distillation](https://mlsanity.com/paper/2205.07062/) (2022)
- [K-space and Image Domain Collaborative Energy based Model for Parallel MRI Reconstruction](https://mlsanity.com/paper/2203.10776/) (2022)
- [Learning to Reconstruct Accelerated MRI Through K-space Cold Diffusion without Noise](https://mlsanity.com/paper/2311.10162/) (2023)
- [Attention Hybrid Variational Net for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2306.12365/) (2023)
- [Deep-ER: Deep Learning ECCENTRIC Reconstruction for fast high-resolution neurometabolic imaging](https://mlsanity.com/paper/2409.18303/) (2024)
- [A Frequency Domain Constraint for Synthetic and Real X-ray Image Super Resolution](https://mlsanity.com/paper/2105.06887/) (2021)
- [Stacked Generative Machine Learning Models for Fast Approximations of Steady-State Navier-Stokes Equations](https://mlsanity.com/paper/2112.06419/) (2021)
- [Universal Generative Modeling in Dual-domain for Dynamic MR Imaging](https://mlsanity.com/paper/2212.07599/) (2022)
- [DeSamba: Decoupled Spectral Adaptive Framework for 3D Multi-Sequence MRI Lesion Classification](https://mlsanity.com/paper/2507.15487/) (2025)
- [Low-Field Magnetic Resonance Image Quality Enhancement using Undersampled k-Space and Out-of-Distribution Generalisation](https://mlsanity.com/paper/2603.14120/) (2026)

## Abstract (arXiv)

Decreasing magnetic resonance (MR) image acquisition times can potentially reduce procedural cost and make MR examinations more accessible. Compressed sensing (CS)-based image reconstruction methods, for example, decrease MR acquisition time by reconstructing high-quality images from data that were originally sampled at rates inferior to the Nyquist-Shannon sampling theorem. In this work we propose a hybrid architecture that works both in the k-space (or frequency-domain) and the image (or spatial) domains. Our network is composed of a complex-valued residual U-net in the k-space domain, an inverse Fast Fourier Transform (iFFT) operation, and a real-valued U-net in the image domain. Our experiments demonstrated, using MR raw k-space data, that the proposed hybrid approach can potentially improve CS reconstruction compared to deep-learning networks that operate only in the image domain. In this study we compare our method with four previously published deep neural networks and examine their ability to reconstruct images that are subsequently used to generate regional volume estimates. We evaluated undersampling ratios of 75% and 80%. Our technique was ranked second in the quantitative analysis, but qualitative analysis indicated that our reconstruction performed the best in hard to reconstruct regions, such as the cerebellum. All images reconstructed with our method were successfully post-processed, and showed good volumetry agreement compared with the fully sampled reconstruction measures.