# Nest-DGIL: Nesterov-optimized Deep Geometric Incremental Learning for CS Image Reconstruction

arXiv: https://arxiv.org/abs/2308.03807 · HTML: https://mlsanity.com/paper/2308.03807/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 72 references that are in the map.
- First posted on arXiv 6 Aug 2023.

## Builds on (most cited first, 28 of 28)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [ESRGAN: Enhanced Super-Resolution Generative Adversarial Networks](https://mlsanity.com/paper/1809.00219/) (2018)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Residual Dense Network for Image Super-Resolution](https://mlsanity.com/paper/1802.08797/) (2018)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [Deep Unfolding Network for Image Super-Resolution](https://mlsanity.com/paper/2003.10428/) (2020)
- [Learned Primal-dual Reconstruction](https://mlsanity.com/paper/1707.06474/) (2017)
- [Low-Dose CT with a Residual Encoder-Decoder Convolutional Neural Network (RED-CNN)](https://mlsanity.com/paper/1702.00288/) (2017)
- [Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restoration](https://mlsanity.com/paper/1508.02848/) (2015)
- [Deep Decoder: Concise Image Representations from Untrained Non-convolutional Networks](https://mlsanity.com/paper/1810.03982/) (2018)
- [Denoising Prior Driven Deep Neural Network for Image Restoration](https://mlsanity.com/paper/1801.06756/) (2018)
- [FISTA-Net: Learning A Fast Iterative Shrinkage Thresholding Network for Inverse Problems in Imaging](https://mlsanity.com/paper/2008.02683/) (2020)
- [AMP-Net: Denoising based Deep Unfolding for Compressive Image Sensing](https://mlsanity.com/paper/2004.10078/) (2020)
- [DU-GAN: Generative Adversarial Networks with Dual-Domain U-Net Based Discriminators for Low-Dose CT Denoising](https://mlsanity.com/paper/2108.10772/) (2021)
- [TorchRadon: Fast Differentiable Routines for Computed Tomography](https://mlsanity.com/paper/2009.14788/) (2020)
- [ISTA-Net++: Flexible Deep Unfolding Network for Compressive Sensing](https://mlsanity.com/paper/2103.11554/) (2021)
- [COAST: COntrollable Arbitrary-Sampling NeTwork for Compressive Sensing](https://mlsanity.com/paper/2107.07225/) (2021)
- [VS-Net: Variable splitting network for accelerated parallel MRI reconstruction](https://mlsanity.com/paper/1907.10033/) (2019)
- [Learning to Invert: Signal Recovery via Deep Convolutional Networks](https://mlsanity.com/paper/1701.03891/) (2017)
- [Hyperparameter Tuning is All You Need for LISTA](https://mlsanity.com/paper/2110.15900/) (2021)
- [CSformer: Bridging Convolution and Transformer for Compressive Sensing](https://mlsanity.com/paper/2112.15299/) (2021)
- [IFR-Net: Iterative Feature Refinement Network for Compressed Sensing MRI](https://mlsanity.com/paper/1909.10856/) (2019)
- [Deep Geometric Distillation Network for Compressive Sensing MRI](https://mlsanity.com/paper/2107.04943/) (2021)
- [An Interpretable MRI Reconstruction Network with Two-grid-cycle Correction and Geometric Prior Distillation](https://mlsanity.com/paper/2205.07062/) (2022)

## Built on by (most cited first, 5 of 5)

- [PRISTA-Net: Deep Iterative Shrinkage Thresholding Network for Coded Diffraction Patterns Phase Retrieval](https://mlsanity.com/paper/2309.04171/) (2023)
- [A Progressive Image Restoration Network for High-order Degradation Imaging in Remote Sensing](https://mlsanity.com/paper/2412.07195/) (2024)
- [A Multi-scale Generalized Shrinkage Threshold Network for Image Blind Deblurring in Remote Sensing](https://mlsanity.com/paper/2309.07524/) (2023)
- [MVMS-RCN: A Dual-Domain Unfolding CT Reconstruction with Multi-sparse-view and Multi-scale Refinement-correction](https://mlsanity.com/paper/2405.17141/) (2024)
- [A Dual-domain Refinement Network with FBP-based Jacobian Learning for Sparse-view Dual-Energy CT Material Decomposition](https://mlsanity.com/paper/2606.30159/) (2026)

## Abstract (arXiv)

Proximal gradient-based optimization is one of the most common strategies to solve inverse problem of images, and it is easy to implement. However, these techniques often generate heavy artifacts in image reconstruction. One of the most popular refinement methods is to fine-tune the regularization parameter to alleviate such artifacts, but it may not always be sufficient or applicable due to increased computational costs. In this work, we propose a deep geometric incremental learning framework based on the second Nesterov proximal gradient optimization. The proposed end-to-end network not only has the powerful learning ability for high-/low-frequency image features, but also can theoretically guarantee that geometric texture details will be reconstructed from preliminary linear reconstruction. Furthermore, it can avoid the risk of intermediate reconstruction results falling outside the geometric decomposition domains and achieve fast convergence. Our reconstruction framework is decomposed into four modules including general linear reconstruction, cascade geometric incremental restoration, Nesterov acceleration, and post-processing. In the image restoration step, a cascade geometric incremental learning module is designed to compensate for missing texture information from different geometric spectral decomposition domains. Inspired by the overlap-tile strategy, we also develop a post-processing module to remove the block effect in patch-wise-based natural image reconstruction. All parameters in the proposed model are learnable, an adaptive initialization technique of physical parameters is also employed to make model flexibility and ensure converging smoothly. We compare the reconstruction performance of the proposed method with existing state-of-the-art methods to demonstrate its superiority. Our source codes are available at https://github.com/fanxiaohong/Nest-DGIL.