Newton Deep Unfolding for Compressed Sensing

Changhua He; Xianchao Xiu

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arXiv · 2609.14391

Newton Deep Unfolding for Compressed Sensing

Changhua He·Xianchao Xiu

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Abstract

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.

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Changhua He, Xianchao Xiu. 2026-09-13. Newton Deep Unfolding for Compressed Sensing. https://arxiv.org/abs/2609.14391

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