# Quaternion-Hadamard Network: A Novel Defense Against Adversarial Attacks with a New Dataset

arXiv: https://arxiv.org/abs/2502.10452 · HTML: https://mlsanity.com/paper/2502.10452/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 77 references that are in the map.
- First posted on arXiv 12 Feb 2025.

## Builds on (most cited first, 30 of 45)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Restormer: Efficient Transformer for High-Resolution Image Restoration](https://mlsanity.com/paper/2111.09881/) (2021)
- [Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examples](https://mlsanity.com/paper/1802.00420/) (2018)
- [ESRGAN: Enhanced Super-Resolution Generative Adversarial Networks](https://mlsanity.com/paper/1809.00219/) (2018)
- [Adversarial Machine Learning at Scale](https://mlsanity.com/paper/1611.01236/) (2016)
- [Universal adversarial perturbations](https://mlsanity.com/paper/1610.08401/) (2016)
- [Square Attack: a query-efficient black-box adversarial attack via random search](https://mlsanity.com/paper/1912.00049/) (2019)
- [Surrogate Gradient Learning in Spiking Neural Networks](https://mlsanity.com/paper/1901.09948/) (2019)
- [Countering Adversarial Images using Input Transformations](https://mlsanity.com/paper/1711.00117/) (2017)
- [Diffusion Models for Adversarial Purification](https://mlsanity.com/paper/2205.07460/) (2022)
- [Benchmarking Single Image Dehazing and Beyond](https://mlsanity.com/paper/1712.04143/) (2017)
- [Defense-GAN: Protecting Classifiers Against Adversarial Attacks Using Generative Models](https://mlsanity.com/paper/1805.06605/) (2018)
- [Multi-Scale Progressive Fusion Network for Single Image Deraining](https://mlsanity.com/paper/2003.10985/) (2020)
- [Vision Transformers for Single Image Dehazing](https://mlsanity.com/paper/2204.03883/) (2022)
- [PixelDefend: Leveraging Generative Models to Understand and Defend against Adversarial Examples](https://mlsanity.com/paper/1710.10766/) (2017)
- [Attention Mechanisms in Computer Vision: A Survey](https://mlsanity.com/paper/2111.07624/) (2021)
- [A study of the effect of JPG compression on adversarial images](https://mlsanity.com/paper/1608.00853/) (2016)
- [On the Robustness of Vision Transformers to Adversarial Examples](https://mlsanity.com/paper/2104.02610/) (2021)
- [Adversarial purification with Score-based generative models](https://mlsanity.com/paper/2106.06041/) (2021)
- [NH-HAZE: An Image Dehazing Benchmark with Non-Homogeneous Hazy and Haze-Free Images](https://mlsanity.com/paper/2005.03560/) (2020)
- [Keeping the Bad Guys Out: Protecting and Vaccinating Deep Learning with JPEG Compression](https://mlsanity.com/paper/1705.02900/) (2017)
- [Curricular Contrastive Regularization for Physics-aware Single Image Dehazing](https://mlsanity.com/paper/2303.14218/) (2023)
- [Deflecting Adversarial Attacks with Pixel Deflection](https://mlsanity.com/paper/1801.08926/) (2018)
- [Image Super-Resolution as a Defense Against Adversarial Attacks](https://mlsanity.com/paper/1901.01677/) (2019)
- [Deep Quaternion Networks](https://mlsanity.com/paper/1712.04604/) (2017)
- [Towards Robust Rain Removal Against Adversarial Attacks: A Comprehensive Benchmark Analysis and Beyond](https://mlsanity.com/paper/2203.16931/) (2022)
- [A comprehensive review of Binary Neural Network](https://mlsanity.com/paper/2110.06804/) (2021)
- [Sparse Sampling Transformer with Uncertainty-Driven Ranking for Unified Removal of Raindrops and Rain Streaks](https://mlsanity.com/paper/2308.14153/) (2023)
- [Reveal of Vision Transformers Robustness against Adversarial Attacks](https://mlsanity.com/paper/2106.03734/) (2021)

## Built on by (most cited first, 1 of 1)

- [Training-Free Color-Aware Adversarial Diffusion Sanitization for Diffusion Stegomalware Defense at Security Gateways](https://mlsanity.com/paper/2512.24499/) (2025)

## Abstract (arXiv)

Adverse-weather image restoration (e.g., rain, snow, haze) models remain highly vulnerable to gradient-based white-box adversarial attacks, wherein minimal loss-aligned perturbations cause substantial degradation in the restored output. This paper presents QHNet, a computationally efficient purification-based defense that precedes the restoration network and targets perturbation suppression in the transform and quaternion domains. QHNet incorporates a Quaternion Hadamard Polynomial Denoising Block (QHPDB) and a Quaternion Denoising Residual Block (QDRB) within an encoder-decoder framework to remove high-frequency adversarial noise while preserving fine structural details. Robustness is evaluated using PSNR and SSIM across rain, snow, and haze removal tasks, and further validated under adaptive, defense-aware white-box attacks employing Projected Gradient Descent (PGD), Backward Pass Differentiable Approximation (BPDA), and Expectation Over Transformation (EOT). Experimental results demonstrate that QHNet delivers superior restoration fidelity and significantly improved robustness compared to state-of-the-art purification baselines, confirming its effectiveness for low-level vision pipelines.