# Thwarting Adversarial Examples: An L0-RobustSparse Fourier Transform

arXiv: https://arxiv.org/abs/1812.05013 · HTML: https://mlsanity.com/paper/1812.05013/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Dec 2018.

## Built on by (most cited first, 13 of 13)

- [Advances in adversarial attacks and defenses in computer vision: A survey](https://mlsanity.com/paper/2108.00401/) (2021)
- [AdvDO: Realistic Adversarial Attacks for Trajectory Prediction](https://mlsanity.com/paper/2209.08744/) (2022)
- [Adversarial Attacks are Reversible with Natural Supervision](https://mlsanity.com/paper/2103.14222/) (2021)
- [Certified Patch Robustness via Smoothed Vision Transformers](https://mlsanity.com/paper/2110.07719/) (2021)
- [PointDP: Diffusion-driven Purification against Adversarial Attacks on 3D Point Cloud Recognition](https://mlsanity.com/paper/2208.09801/) (2022)
- [Projected Randomized Smoothing for Certified Adversarial Robustness](https://mlsanity.com/paper/2309.13794/) (2023)
- [The art of defense: letting networks fool the attacker](https://mlsanity.com/paper/2104.02963/) (2021)
- [EvoBA: An Evolution Strategy as a Strong Baseline forBlack-Box Adversarial Attacks](https://mlsanity.com/paper/2107.05754/) (2021)
- [FIMBA: Evaluating the Robustness of AI in Genomics via Feature Importance Adversarial Attacks](https://mlsanity.com/paper/2401.10657/) (2024)
- [Denoised Internal Models: a Brain-Inspired Autoencoder against Adversarial Attacks](https://mlsanity.com/paper/2111.10844/) (2021)
- [Robust width: A lightweight and certifiable adversarial defense](https://mlsanity.com/paper/2405.15971/) (2024)
- [Introducing the DOME Activation Functions](https://mlsanity.com/paper/2109.14798/) (2021)
- [GReAT: A Graph Regularized Adversarial Training Method](https://mlsanity.com/paper/2310.05336/) (2023)

## Abstract (arXiv)

We give a new algorithm for approximating the Discrete Fourier transform of an approximately sparse signal that has been corrupted by worst-case L0 noise, namely a bounded number of coordinates of the signal have been corrupted arbitrarily. Our techniques generalize to a wide range of linear transformations that are used in data analysis such as the Discrete Cosine and Sine transforms, the Hadamard transform, and their high-dimensional analogs. We use our algorithm to successfully defend against well known L0 adversaries in the setting of image classification. We give experimental results on the Jacobian-based Saliency Map Attack (JSMA) and the Carlini Wagner (CW) L0 attack on the MNIST and Fashion-MNIST datasets as well as the Adversarial Patch on the ImageNet dataset.