# CLEAR: Complex Learned Explicit Analytical Regularization for Ultra-Accelerated 4D Flow CMR Reconstruction

arXiv: https://arxiv.org/abs/2609.22950 · HTML: https://mlsanity.com/paper/2609.22950/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 31 references that are in the map.
- First posted on arXiv 19 Sep 2026.

## Builds on (most cited first, 15 of 15)

- [Convolutional Recurrent Neural Networks for Dynamic MR Image Reconstruction](https://mlsanity.com/paper/1712.01751/) (2017)
- [JFB: Jacobian-Free Backpropagation for Implicit Networks](https://mlsanity.com/paper/2103.12803/) (2021)
- [A Neural-Network-Based Convex Regularizer for Inverse Problems](https://mlsanity.com/paper/2211.12461/) (2022)
- [Learning Weakly Convex Regularizers for Convergent Image-Reconstruction Algorithms](https://mlsanity.com/paper/2308.10542/) (2023)
- [One-step differentiation of iterative algorithms](https://mlsanity.com/paper/2305.13768/) (2023)
- [One-dimensional Deep Low-rank and Sparse Network for Accelerated MRI](https://mlsanity.com/paper/2112.04721/) (2021)
- [One for Multiple: Physics-informed Synthetic Data Boosts Generalizable Deep Learning for Fast MRI Reconstruction](https://mlsanity.com/paper/2307.13220/) (2023)
- [Learning Regularization Functionals for Inverse Problems: A Comparative Study](https://mlsanity.com/paper/2510.01755/) (2025)
- [Deep variational network for rapid 4D flow MRI reconstruction](https://mlsanity.com/paper/2004.09610/) (2020)
- [Towards Modality- and Sampling-Universal Learning Strategies for Accelerating Cardiovascular Imaging: Summary of the CMRxRecon2024 Challenge](https://mlsanity.com/paper/2503.03971/) (2025)
- [Deep Separable Spatiotemporal Learning for Fast Dynamic Cardiac MRI](https://mlsanity.com/paper/2402.15939/) (2024)
- [FlowMRI-Net: A Generalizable Self-Supervised 4D Flow MRI Reconstruction network](https://mlsanity.com/paper/2410.08856/) (2024)
- [Enabling Ultra-Fast Cardiovascular Imaging Across Heterogeneous Clinical Environments with A Generalist Foundation Model and Multimodal Database](https://mlsanity.com/paper/2512.21652/) (2025)
- [Extreme Cardiac MRI Analysis under Respiratory Motion: Results of the CMRxMotion Challenge](https://mlsanity.com/paper/2507.19165/) (2025)
- [Weakly Convex Ridge Regularization for 3D Non-Cartesian MRI Reconstruction](https://mlsanity.com/paper/2603.27158/) (2026)

## Abstract (arXiv)

While compressed-sensing regularizers enable interpretable reconstruction of 4D Flow CMR through transparent variational objectives, their hand-crafted nature is too restrictive under high acceleration. State-of-the-art learning-based approaches mitigate this, but typically encode regularization implicitly through unrolled network modules, which limits their interpretability. To address this limitation, we propose CLEAR, designed to combine the interpretability of compressed sensing with the flexibility of learned models. To the best of our knowledge, it is the first learned regularizer for a 4D reconstruction task. In the ultra-accelerated (10×)--(50×) regime of the CMRx4DFlow2026 challenge, CLEAR outperforms compressed sensing locally low-rank (LLR) and the popular variational network FlowVN, while using less than 10k parameters and preserving an interpretable regularization structure.