# Newton Deep Unfolding for Compressed Sensing

arXiv: https://arxiv.org/abs/2609.14391 · HTML: https://mlsanity.com/paper/2609.14391/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 32 references that are in the map.
- First posted on arXiv 13 Sep 2026.

## Builds on (most cited first, 9 of 9)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [ESRGAN: Enhanced Super-Resolution Generative Adversarial Networks](https://mlsanity.com/paper/1809.00219/) (2018)
- [AMP-Net: Denoising based Deep Unfolding for Compressive Image Sensing](https://mlsanity.com/paper/2004.10078/) (2020)
- [Learned D-AMP: Principled Neural Network based Compressive Image Recovery](https://mlsanity.com/paper/1704.06625/) (2017)
- [ISTA-Net++: Flexible Deep Unfolding Network for Compressive Sensing](https://mlsanity.com/paper/2103.11554/) (2021)
- [Deep Networks for Compressed Image Sensing](https://mlsanity.com/paper/1707.07119/) (2017)
- [Optimization-Inspired Cross-Attention Transformer for Compressive Sensing](https://mlsanity.com/paper/2304.13986/) (2023)
- [Fast Hierarchical Deep Unfolding Network for Image Compressed Sensing](https://mlsanity.com/paper/2208.01827/) (2022)

## Abstract (arXiv)

Compressed sensing (CS) reconstructs images from highly limited measurements, but existing deep unfolding methods are typically driven by first-order optimization and weakly exploit the optimization states generated during reconstruction. To address these limitations, we propose a Newton deep unfolding network (NDU-Net), which, to the best of our knowledge, is the first deep unfolding framework that leverages second-order optimization for CS reconstruction. Specifically, NDU-Net introduces a Newton update (NU) module to estimate Newton-type update directions and generate optimization states that characterize the current reconstruction process. Furthermore, a Newton-guided multi-scale prior (MP) module is designed to incorporate these optimization states into multi-scale feature restoration, thereby enabling the learned prior to adapt to the current reconstruction stage. Experimental results under different CS ratios confirm that our proposed NDU-Net achieves promising reconstruction performance and exhibits enhanced robustness. Our code is available at https://github.com/xianchaoxiu/DNU-Net.