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

arXiv:2603.27158v3 Announce Type: replace Abstract: 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.

Related

• Joint Supervised and Self-Supervised Training with Acquisition-Robust Techniques for Accelerated 4D Flow MRI Reconstruction
• CLEAR: Complex Learned Explicit Analytical Regularization for Ultra-Accelerated 4D Flow CMR Reconstruction
• UMPIRE-Net: Unrolled Magnitude-Phase Regularization Network for Accelerated MRI
• Interlaced R2D2 DNN Series for Scalable Non-Cartesian MRI with Sensitivity Self-calibration

Source: arXiv cs.CV | 2026-10-14