# A Complex Quasi-Newton Proximal Method for Image Reconstruction in Compressed Sensing MRI

arXiv: https://arxiv.org/abs/2303.02586 · HTML: https://mlsanity.com/paper/2303.02586/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Mar 2023.

## Built on by (most cited first, 8 of 8)

- [Learning Image Priors through Patch-based Diffusion Models for Solving Inverse Problems](https://mlsanity.com/paper/2406.02462/) (2024)
- [Patch-Based Diffusion Models Beat Whole-Image Models for Mismatched Distribution Inverse Problems](https://mlsanity.com/paper/2410.11730/) (2024)
- [Bayesian Uncertainty-Aware MRI Reconstruction](https://mlsanity.com/paper/2603.13439/) (2026)
- [MCU-Net: A Multi-prior Collaborative Deep Unfolding Network with Gates-controlled Spatial Attention for Accelerated MR Image Reconstruction](https://mlsanity.com/paper/2402.03383/) (2024)
- [Local Patches Meet Global Context: Scalable 3D Diffusion Priors for Computed Tomography Reconstruction](https://mlsanity.com/paper/2512.18161/) (2025)
- [A New k-Space Model for Non-Cartesian Fourier Imaging](https://mlsanity.com/paper/2505.05647/) (2025)
- [Low-Field Magnetic Resonance Image Enhancement using Undersampled k-Space](https://mlsanity.com/paper/2603.14125/) (2026)
- [Trustworthy MRI Reconstruction via Bayesian Uncertainty Quantification with Sparsity Prior Models](https://mlsanity.com/paper/2606.17343/) (2026)

## Abstract (arXiv)

Model-based methods are widely used for reconstruction in compressed sensing (CS) magnetic resonance imaging (MRI), using regularizers to describe the images of interest. The reconstruction process is equivalent to solving a composite optimization problem. Accelerated proximal methods (APMs) are very popular approaches for such problems. This paper proposes a complex quasi-Newton proximal method (CQNPM) for the wavelet and total variation based CS MRI reconstruction. Compared with APMs, CQNPM requires fewer iterations to converge but needs to compute a more challenging proximal mapping called weighted proximal mapping (WPM). To make CQNPM more practical, we propose efficient methods to solve the related WPM. Numerical experiments on reconstructing non-Cartesian MRI data demonstrate the effectiveness and efficiency of CQNPM.