# Thwarting Adversarial Examples: An $L\_0$-RobustSparse Fourier Transform

Source: [Thwarting Adversarial Examples: An $L\_0$-RobustSparse Fourier Transform](<https://www.sota2.com/research/paper/68fa65341e209131cea08f0a>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T21:21:52.901Z

Authors: Mitali Bafna, Jack Murtagh, Nikhil Vyas

Published: 2018-12-12T16:36:14.000Z

## Abstract

We give a new algorithm for approximating the Discrete Fourier transform of an approximately sparse signal that has been corrupted by worst-case $L\_0$ 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 $L\_0$ adversaries in the setting of image classification. We give experimental results on the Jacobian-based Saliency Map Attack (JSMA) and the Carlini Wagner (CW) $L\_0$ attack on the MNIST and Fashion-MNIST datasets as well as the Adversarial Patch on the ImageNet dataset.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1812.05013>)

[PDF](<https://arxiv.org/pdf/1812.05013.pdf>)