Low-rank matrix recovery with total generalized variation for defending adversarial examples

Abstract

Low-rank matrix decomposition with first-order total variation (TV) regularization exhibits excellent performance in exploration of image structure. Taking advantage of its excellent performance in image denoising, we apply it to improve the robustness of deep neural networks. However, although TV regularization can improve the robustness of the model, it reduces the accuracy of normal samples due to its over-smoothing. In our work, we develop a new low-rank matrix recovery model, called LRTGV, which incorporates total generalized variation (TGV) regularization into the reweighted low-rank matrix recovery model. In the proposed model, TGV is used to better reconstruct texture information without over-smoothing. The reweighted nuclear norm and L₁-norm can enhance the global structure information. Thus, the proposed LRTGV can destroy the structure of adversarial noise while re-enhancing the global structure and local texture of the image. To solve the challenging optimal model issue, we propose an algorithm based on the alternating direction method of multipliers. Experimental results show that the proposed algorithm has a certain defense capability against black-box attacks, and outperforms state-of-the-art low-rank matrix recovery methods in image restoration.

摘要

一阶全变分(TV)正则化的低秩矩阵分解在恢复图像结构上表现出优异性能。利用全变分在图像去噪方面的优异性能,提高深度神经网络鲁棒性。然而,尽管一阶全变分正则化可以提高模型鲁棒性,但其过度平滑降低了干净样本的准确率。本文提出一种新的低秩矩阵恢复模型,称为LRTGV,该模型将广义全变分(TGV)正则化引入到重加权低秩矩阵恢复模型。在所构建的模型中,TGV可以在不过度平滑的情况下更好地重建图像纹理信息。重加权核范数和L1范数可以增强全局结构信息。因此,本文所提出的LRTGV模型在破坏对抗噪声结构的同时能增强图像全局结构和局部纹理信息。为解决具有挑战性的最优模型问题,本文提出一种基于交替方向乘子法的算法。实验结果表明,该算法对黑盒攻击具有一定防御能力,并且在图像恢复方面优于现有低秩矩阵恢复方法。