# Complementary Time-Frequency Domain Networks for Dynamic Parallel MR Image Reconstruction

arXiv: https://arxiv.org/abs/2012.11974 · HTML: https://mlsanity.com/paper/2012.11974/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Dec 2020.

## Built on by (most cited first, 10 of 10)

- [CMRxRecon: An open cardiac MRI dataset for the competition of accelerated image reconstruction](https://mlsanity.com/paper/2309.10836/) (2023)
- [Implicit Neural Networks with Fourier-Feature Inputs for Free-breathing Cardiac MRI Reconstruction](https://mlsanity.com/paper/2305.06822/) (2023)
- [Learning-based and unrolled motion-compensated reconstruction for cardiac MR CINE imaging](https://mlsanity.com/paper/2209.03671/) (2022)
- [Dual-Domain Reconstruction Networks with V-Net and K-Net for fast MRI](https://mlsanity.com/paper/2203.05725/) (2022)
- [Motion-compensated MR CINE reconstruction with reconstruction-driven motion estimation](https://mlsanity.com/paper/2302.02504/) (2023)
- [HierAdaptMR: Cross-Center Cardiac MRI Reconstruction with Hierarchical Feature Adapters](https://mlsanity.com/paper/2508.13026/) (2025)
- [Artificial Intelligence-Based Image Reconstruction in Cardiac Magnetic Resonance](https://mlsanity.com/paper/2209.10298/) (2022)
- [The Challenge of Fetal Cardiac MRI Reconstruction Using Deep Learning](https://mlsanity.com/paper/2308.07885/) (2023)
- [k-t CLAIR: Self-Consistency Guided Multi-Prior Learning for Dynamic Parallel MR Image Reconstruction](https://mlsanity.com/paper/2310.11050/) (2023)
- [Advancing MRI Reconstruction: A Systematic Review of Deep Learning and Compressed Sensing Integration](https://mlsanity.com/paper/2501.14158/) (2025)

## Abstract (arXiv)

Purpose: To introduce a novel deep learning based approach for fast and high-quality dynamic multi-coil MR reconstruction by learning a complementary time-frequency domain network that exploits spatio-temporal correlations simultaneously from complementary domains. Theory and Methods: Dynamic parallel MR image reconstruction is formulated as a multi-variable minimisation problem, where the data is regularised in combined temporal Fourier and spatial (x-f) domain as well as in spatio-temporal image (x-t) domain. An iterative algorithm based on variable splitting technique is derived, which alternates among signal de-aliasing steps in x-f and x-t spaces, a closed-form point-wise data consistency step and a weighted coupling step. The iterative model is embedded into a deep recurrent neural network which learns to recover the image via exploiting spatio-temporal redundancies in complementary domains. Results: Experiments were performed on two datasets of highly undersampled multi-coil short-axis cardiac cine MRI scans. Results demonstrate that our proposed method outperforms the current state-of-the-art approaches both quantitatively and qualitatively. The proposed model can also generalise well to data acquired from a different scanner and data with pathologies that were not seen in the training set. Conclusion: The work shows the benefit of reconstructing dynamic parallel MRI in complementary time-frequency domains with deep neural networks. The method can effectively and robustly reconstruct high-quality images from highly undersampled dynamic multi-coil data (16 × and 24 × yielding 15s and 10s scan times respectively) with fast reconstruction speed (2.8s). This could potentially facilitate achieving fast single-breath-hold clinical 2D cardiac cine imaging.