# A Tunable Despeckling Neural Network Stabilized via Diffusion Equation

arXiv: https://arxiv.org/abs/2411.15921 · HTML: https://mlsanity.com/paper/2411.15921/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 70 references that are in the map.
- First posted on arXiv 24 Nov 2024.

## Builds on (most cited first, 25 of 25)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Adversarial examples in the physical world](https://mlsanity.com/paper/1607.02533/) (2016)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Remote Sensing Image Scene Classification: Benchmark and State of the Art](https://mlsanity.com/paper/1703.00121/) (2017)
- [Adversarial Training for Free!](https://mlsanity.com/paper/1904.12843/) (2019)
- [Lipschitz regularity of deep neural networks: analysis and efficient estimation](https://mlsanity.com/paper/1805.10965/) (2018)
- [Regularisation of Neural Networks by Enforcing Lipschitz Continuity](https://mlsanity.com/paper/1804.04368/) (2018)
- [Deep Neural Networks Motivated by Partial Differential Equations](https://mlsanity.com/paper/1804.04272/) (2018)
- [FloodNet: A High Resolution Aerial Imagery Dataset for Post Flood Scene Understanding](https://mlsanity.com/paper/2012.02951/) (2020)
- [Neural SDE: Stabilizing Neural ODE Networks with Stochastic Noise](https://mlsanity.com/paper/1906.02355/) (2019)
- [SAR image despeckling through convolutional neural networks](https://mlsanity.com/paper/1704.00275/) (2017)
- [CLIP: Cheap Lipschitz Training of Neural Networks](https://mlsanity.com/paper/2103.12531/) (2021)
- [Equivariant plug-and-play image reconstruction](https://mlsanity.com/paper/2312.01831/) (2023)
- [Deep Neural Networks with Trainable Activations and Controlled Lipschitz Constant](https://mlsanity.com/paper/2001.06263/) (2020)
- [SAR Image Despeckling Using a Convolutional Neural Network](https://mlsanity.com/paper/1706.00552/) (2017)
- [Lipschitz regularized Deep Neural Networks generalize and are adversarially robust](https://mlsanity.com/paper/1808.09540/) (2018)
- [Transformer-based SAR Image Despeckling](https://mlsanity.com/paper/2201.09355/) (2022)
- [Towards Adversarially Robust Deep Image Denoising](https://mlsanity.com/paper/2201.04397/) (2022)
- [Coupling Model-Driven and Data-Driven Methods for Remote Sensing Image Restoration and Fusion](https://mlsanity.com/paper/2108.06073/) (2021)
- [Learning a Dilated Residual Network for SAR Image Despeckling](https://mlsanity.com/paper/1709.02898/) (2017)
- [Large Norms of CNN Layers Do Not Hurt Adversarial Robustness](https://mlsanity.com/paper/2009.08435/) (2020)
- [Evaluating Similitude and Robustness of Deep Image Denoising Models via Adversarial Attack](https://mlsanity.com/paper/2306.16050/) (2023)

## Built on by (most cited first, 2 of 2)

- [γ-Bridge: A Look-Parametric Diffusion Bridge](https://mlsanity.com/paper/2607.22719/) (2026)
- [Closed-Form Nonlocal Shrinkage for Multiplicative Image Denoising and SAR Despeckling](https://mlsanity.com/paper/2608.15028/) (2026)

## Abstract (arXiv)

The removal of multiplicative Gamma noise is a critical research area in the application of synthetic aperture radar (SAR) imaging, where neural networks serve as a potent tool. However, real-world data often diverges from theoretical models, exhibiting various disturbances, which makes the neural network less effective. Adversarial attacks can be used as a criterion for judging the adaptability of neural networks to real data, since they can find the most extreme perturbations that make neural networks ineffective. In this work, we propose a tunable, regularized neural network framework that unrolls a shallow neural denoising block and a diffusion regularization block into a single network for end-to-end training. The linear heat equation, known for its inherent smoothness and low-pass filtering properties, is adopted as the diffusion regularization block. The smoothness of our outputs is controlled by a single time step hyperparameter that can be adjusted dynamically. The stability and convergence of our model are theoretically proven. Experimental results demonstrate that the proposed model effectively eliminates high-frequency oscillations induced by adversarial attacks. Finally, the proposed model is benchmarked against several state-of-the-art denoising methods on simulated images, adversarial samples, and real SAR images, achieving superior performance in both quantitative and visual evaluations.