# Complex Fully Convolutional Neural Networks for MR Image Reconstruction

arXiv: https://arxiv.org/abs/1807.03343 · HTML: https://mlsanity.com/paper/1807.03343/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jul 2018.

## Built on by (most cited first, 12 of 12)

- [Adaptive Diffusion Priors for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2207.05876/) (2022)
- [Co-domain Symmetry for Complex-Valued Deep Learning](https://mlsanity.com/paper/2112.01525/) (2021)
- [Neural Networks with Complex-Valued Weights Have No Spurious Local Minima](https://mlsanity.com/paper/2103.07287/) (2021)
- [From CNNs to Shift-Invariant Twin Models Based on Complex Wavelets](https://mlsanity.com/paper/2212.00394/) (2022)
- [Biomedical Image Reconstruction: A Survey](https://mlsanity.com/paper/2301.11813/) (2023)
- [Accelerated Proton Resonance Frequency-based Magnetic Resonance Thermometry by Optimized Deep Learning Method](https://mlsanity.com/paper/2407.03308/) (2024)
- [Dual-domain Multi-path Self-supervised Diffusion Model for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2503.18836/) (2025)
- [Phase-Aware Deep Learning with Complex-Valued CNNs for Audio Signal Applications](https://mlsanity.com/paper/2510.09926/) (2025)
- [Shift-Equivariant Complex-Valued Convolutional Neural Networks](https://mlsanity.com/paper/2511.21250/) (2025)
- [Frequency Error-Guided Under-sampling Optimization for Multi-Contrast MRI Reconstruction](https://mlsanity.com/paper/2601.09316/) (2026)
- [Exploring Polarimetric Properties Preservation during Reconstruction of PolSAR images using Complex-valued Convolutional Neural Networks](https://mlsanity.com/paper/2602.07094/) (2026)
- [Deep Psychovisual Image Representations](https://mlsanity.com/paper/2605.29260/) (2026)

## Abstract (arXiv)

Undersampling the k-space data is widely adopted for acceleration of Magnetic Resonance Imaging (MRI). Current deep learning based approaches for supervised learning of MRI image reconstruction employ real-valued operations and representations by treating complex valued k-space/spatial-space as real values. In this paper, we propose complex dense fully convolutional neural network (mathbbCDFNet) for learning to de-alias the reconstruction artifacts within undersampled MRI images. We fashioned a densely-connected fully convolutional block tailored for complex-valued inputs by introducing dedicated layers such as complex convolution, batch normalization, non-linearities etc. mathbbCDFNet leverages the inherently complex-valued nature of input k-space and learns richer representations. We demonstrate improved perceptual quality and recovery of anatomical structures through mathbbCDFNet in contrast to its real-valued counterparts.