Modeling and Energy Analysis of Adversarial Perturbations in Deep Image Classification Security

Despite the great success of deep neural networks (DNNs) in computer vision, they are vulnerable to adversarial attacks. Given a well-trained DNN and an image$x$, a malicious and imperceptible perturbation$\varepsilon$can be easily crafted and added to$x$to generate an adversarial example$x^{\prime}$. The output of the DNN in response to$x^{\prime}$will be different from that of the DNN in response to$x$• To shed light on how to defend DNNs against such adversarial attacks, in this paper, we apply statistical methods to model and analyze adversarial perturbations$\varepsilon$crafted by FGSM, PGD, and CW attacks. It is shown statistically that (1) the adversarial perturbations$\varepsilon$crafted by FGSM, PGD, and CW attacks can all be modelled in the Discrete Cosine Transform (DCT) domain by the Transparent Composite Model (TCM) based on generalized Gaussian (GGTCM); (2) CW attack puts more perturbation energy in the background of an image than in the object of the image, while there is no such distinction for FGSM and PGD attacks; and (3) the energy of adversarial perturbation in the case of CW attack is more concentrated on DC components than in the case of FGSM and PGD attacks.