# Weakly Convex Ridge Regularization for 3D Non-Cartesian MRI Reconstruction

arXiv: https://arxiv.org/abs/2603.27158 · HTML: https://mlsanity.com/paper/2603.27158/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 68 references that are in the map.
- First posted on arXiv 28 Mar 2026.

## Builds on (most cited first, 25 of 25)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [Plug-and-Play Image Restoration with Deep Denoiser Prior](https://mlsanity.com/paper/2008.13751/) (2020)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [Learning a Variational Network for Reconstruction of Accelerated MRI Data](https://mlsanity.com/paper/1704.00447/) (2017)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [AdaBelief Optimizer: Adapting Stepsizes by the Belief in Observed Gradients](https://mlsanity.com/paper/2010.07468/) (2020)
- [Learned Primal-dual Reconstruction](https://mlsanity.com/paper/1707.06474/) (2017)
- [Gradient Step Denoiser for convergent Plug-and-Play](https://mlsanity.com/paper/2110.03220/) (2021)
- [Regularization by Denoising: Clarifications and New Interpretations](https://mlsanity.com/paper/1806.02296/) (2018)
- [Proximal Denoiser for Convergent Plug-and-Play Optimization with Nonconvex Regularization](https://mlsanity.com/paper/2201.13256/) (2022)
- [Total Deep Variation for Linear Inverse Problems](https://mlsanity.com/paper/2001.05005/) (2020)
- [A Neural-Network-Based Convex Regularizer for Inverse Problems](https://mlsanity.com/paper/2211.12461/) (2022)
- [The troublesome kernel -- On hallucinations, no free lunches and the accuracy-stability trade-off in inverse problems](https://mlsanity.com/paper/2001.01258/) (2020)
- [Learning Weakly Convex Regularizers for Convergent Image-Reconstruction Algorithms](https://mlsanity.com/paper/2308.10542/) (2023)
- [DeepInverse: A Python package for solving imaging inverse problems with deep learning](https://mlsanity.com/paper/2505.20160/) (2025)
- [Recovery Analysis for Plug-and-Play Priors using the Restricted Eigenvalue Condition](https://mlsanity.com/paper/2106.03668/) (2021)
- [Regularising Inverse Problems with Generative Machine Learning Models](https://mlsanity.com/paper/2107.11191/) (2021)
- [Stable Deep MRI Reconstruction using Generative Priors](https://mlsanity.com/paper/2210.13834/) (2022)
- [Multi-Coil MRI Reconstruction Challenge -- Assessing Brain MRI Reconstruction Models and their Generalizability to Varying Coil Configurations](https://mlsanity.com/paper/2011.07952/) (2020)
- [Deep Equilibrium Learning of Explicit Regularizers for Imaging Inverse Problems](https://mlsanity.com/paper/2303.05386/) (2023)
- [Learning Regularization Functionals for Inverse Problems: A Comparative Study](https://mlsanity.com/paper/2510.01755/) (2025)
- [Neural-network-based regularization methods for inverse problems in imaging](https://mlsanity.com/paper/2312.14849/) (2023)
- [Stability of Data-Dependent Ridge-Regularization for Inverse Problems](https://mlsanity.com/paper/2406.12289/) (2024)

## Built on by (most cited first, 1 of 1)

- [CLEAR: Complex Learned Explicit Analytical Regularization for Ultra-Accelerated 4D Flow CMR Reconstruction](https://mlsanity.com/paper/2609.22950/) (2026)

## Abstract (arXiv)

While highly accelerated non-Cartesian acquisition protocols significantly reduce scan time, they often entail long reconstruction delays. Deep learning based reconstruction methods can alleviate this, but often lack stability and robustness to distribution shifts. As an alternative, we train a rotation invariant weakly convex ridge regularizer (WCRR). The resulting variational reconstruction approach is benchmarked against state of the art methods on retrospectively simulated data and (out of distribution) on prospective GoLF SPARKLING and CAIPIRINHA acquisitions. Our approach consistently outperforms widely used baselines and achieves performance comparable to Plug and Play reconstruction with a state of the art 3D DRUNet denoiser, while offering substantially improved computational efficiency and robustness to acquisition changes. In summary, WCRR unifies the strengths of principled variational methods and modern deep learning based approaches.