# PWAVEP: Purifying Imperceptible Adversarial Perturbations in 3D Point Clouds via Spectral Graph Wavelets

arXiv: https://arxiv.org/abs/2602.03333 · HTML: https://mlsanity.com/paper/2602.03333/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 44 references that are in the map.
- First posted on arXiv 3 Feb 2026.

## Builds on (most cited first, 20 of 20)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Multi-View 3D Object Detection Network for Autonomous Driving](https://mlsanity.com/paper/1611.07759/) (2016)
- [Deep Learning for 3D Point Clouds: A Survey](https://mlsanity.com/paper/1912.12033/) (2019)
- [Rethinking Network Design and Local Geometry in Point Cloud: A Simple Residual MLP Framework](https://mlsanity.com/paper/2202.07123/) (2022)
- [Walk in the Cloud: Learning Curves for Point Clouds Shape Analysis](https://mlsanity.com/paper/2105.01288/) (2021)
- [Generating 3D Adversarial Point Clouds](https://mlsanity.com/paper/1809.07016/) (2018)
- [Higher-order organization of complex networks](https://mlsanity.com/paper/1612.08447/) (2016)
- [Extending Adversarial Attacks and Defenses to Deep 3D Point Cloud Classifiers](https://mlsanity.com/paper/1901.03006/) (2019)
- [Adversarial Attack and Defense on Point Sets](https://mlsanity.com/paper/1902.10899/) (2019)
- [Shape-invariant 3D Adversarial Point Clouds](https://mlsanity.com/paper/2203.04041/) (2022)
- [Deep frequency principle towards understanding why deeper learning is faster](https://mlsanity.com/paper/2007.14313/) (2020)
- [Imperceptible and Robust Backdoor Attack in 3D Point Cloud](https://mlsanity.com/paper/2208.08052/) (2022)
- [Robust Structured Declarative Classifiers for 3D Point Clouds: Defending Adversarial Attacks with Implicit Gradients](https://mlsanity.com/paper/2203.15245/) (2022)
- [PointDP: Diffusion-driven Purification against Adversarial Attacks on 3D Point Cloud Recognition](https://mlsanity.com/paper/2208.09801/) (2022)
- [PointCAT: Contrastive Adversarial Training for Robust Point Cloud Recognition](https://mlsanity.com/paper/2209.07788/) (2022)
- [Ada3Diff: Defending against 3D Adversarial Point Clouds via Adaptive Diffusion](https://mlsanity.com/paper/2211.16247/) (2022)
- [STBA: Towards Evaluating the Robustness of DNNs for Query-Limited Black-box Scenario](https://mlsanity.com/paper/2404.00362/) (2024)

## Abstract (arXiv)

Recent progress in adversarial attacks on 3D point clouds, particularly in achieving spatial imperceptibility and high attack performance, presents significant challenges for defenders. Current defensive approaches remain cumbersome, often requiring invasive model modifications, expensive training procedures or auxiliary data access. To address these threats, in this paper, we propose a plug-and-play and non-invasive defense mechanism in the spectral domain, grounded in a theoretical and empirical analysis of the relationship between imperceptible perturbations and high-frequency spectral components. Building upon these insights, we introduce a novel purification framework, termed PWAVEP, which begins by computing a spectral graph wavelet domain saliency score and local sparsity score for each point. Guided by these values, PWAVEP adopts a hierarchical strategy, it eliminates the most salient points, which are identified as hardly recoverable adversarial outliers. Simultaneously, it applies a spectral filtering process to a broader set of moderately salient points. This process leverages a graph wavelet transform to attenuate high-frequency coefficients associated with the targeted points, thereby effectively suppressing adversarial noise. Extensive evaluations demonstrate that the proposed PWAVEP achieves superior accuracy and robustness compared to existing approaches, advancing the state-of-the-art in 3D point cloud purification. Code and datasets are available at https://github.com/a772316182/pwavep