# Structure-Preserving Progressive Low-rank Image Completion for Defending Adversarial Attacks

arXiv: https://arxiv.org/abs/2103.02781 · HTML: https://mlsanity.com/paper/2103.02781/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 33 references that are in the map.
- First posted on arXiv 4 Mar 2021.

## Builds on (most cited first, 17 of 17)

- [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)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [ImageNet-trained CNNs are biased towards texture; increasing shape bias improves accuracy and robustness](https://mlsanity.com/paper/1811.12231/) (2018)
- [Ensemble Adversarial Training: Attacks and Defenses](https://mlsanity.com/paper/1705.07204/) (2017)
- [Countering Adversarial Images using Input Transformations](https://mlsanity.com/paper/1711.00117/) (2017)
- [Defense-GAN: Protecting Classifiers Against Adversarial Attacks Using Generative Models](https://mlsanity.com/paper/1805.06605/) (2018)
- [Feature Denoising for Improving Adversarial Robustness](https://mlsanity.com/paper/1812.03411/) (2018)
- [PixelDefend: Leveraging Generative Models to Understand and Defend against Adversarial Examples](https://mlsanity.com/paper/1710.10766/) (2017)
- [Adversarial Logit Pairing](https://mlsanity.com/paper/1803.06373/) (2018)
- [Feature Distillation: DNN-Oriented JPEG Compression Against Adversarial Examples](https://mlsanity.com/paper/1803.05787/) (2018)
- [Defense Against Adversarial Attacks Using Feature Scattering-based Adversarial Training](https://mlsanity.com/paper/1907.10764/) (2019)
- [Metric Learning for Adversarial Robustness](https://mlsanity.com/paper/1909.00900/) (2019)
- [ME-Net: Towards Effective Adversarial Robustness with Matrix Estimation](https://mlsanity.com/paper/1905.11971/) (2019)
- [Adversarial Defense by Stratified Convolutional Sparse Coding](https://mlsanity.com/paper/1812.00037/) (2018)
- [Defending against adversarial attacks by randomized diversification](https://mlsanity.com/paper/1904.00689/) (2019)
- [Smoothed Low Rank and Sparse Matrix Recovery by Iteratively Reweighted Least Squares Minimization](https://mlsanity.com/paper/1401.7413/) (2014)

## Abstract (arXiv)

Deep neural networks recognize objects by analyzing local image details and summarizing their information along the inference layers to derive the final decision. Because of this, they are prone to adversarial attacks. Small sophisticated noise in the input images can accumulate along the network inference path and produce wrong decisions at the network output. On the other hand, human eyes recognize objects based on their global structure and semantic cues, instead of local image textures. Because of this, human eyes can still clearly recognize objects from images which have been heavily damaged by adversarial attacks. This leads to a very interesting approach for defending deep neural networks against adversarial attacks. In this work, we propose to develop a structure-preserving progressive low-rank image completion (SPLIC) method to remove unneeded texture details from the input images and shift the bias of deep neural networks towards global object structures and semantic cues. We formulate the problem into a low-rank matrix completion problem with progressively smoothed rank functions to avoid local minimums during the optimization process. Our experimental results demonstrate that the proposed method is able to successfully remove the insignificant local image details while preserving important global object structures. On black-box, gray-box, and white-box attacks, our method outperforms existing defense methods (by up to 12.6%) and significantly improves the adversarial robustness of the network.