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We propose the scheme that mitigates the adversarial perturbation $\epsilon$on the adversarial example $X_{adv}$ ($=$ $X$ $\pm$ $\epsilon$, $X$ is a benignsample) by subtracting the estimated perturbation $\hat{\epsilon}$ from $X$ $+$$\epsilon$ and adding $\hat{\epsilon}$ to $X$ $-$ $\epsilon$. The estimatedperturbation $\hat{\epsilon}$ comes from the difference between $X_{adv}$ andits moving-averaged outcome $W_{avg}*X_{adv}$ where $W_{avg}$ is $N \times N$moving average kernel that all the coefficients are one. Usually, the adjacentsamples of an image are close to each other such that we can let $X$ $\approx$$W_{avg}*X$ (naming this relation after X-MAS[X minus Moving AveragedSamples]). By doing that, we can make the estimated perturbation$\hat{\epsilon}$ falls within the range of $\epsilon$. The scheme is alsoextended to do the multi-level mitigation by configuring the mitigatedadversarial example $X_{adv}$ $\pm$ $\hat{\epsilon}$ as a new adversarialexample to be mitigated. The multi-level mitigation gets $X_{adv}$ closer to$X$ with a smaller (i.e. mitigated) perturbation than original unmitigatedperturbation by setting the moving averaged adversarial sample $W_{avg} *X_{adv}$ (which has the smaller perturbation than $X_{adv}$ if $X$ $\approx$$W_{avg}*X$) as the boundary condition that the multi-level mitigation cannotcross over (i.e. decreasing $\epsilon$ cannot go below and increasing$\epsilon$ cannot go beyond). With the multi-level mitigation, we can get highprediction accuracies even in the adversarial example having a largeperturbation (i.e. $\epsilon$ $>$ $16$). The proposed scheme is evaluated withadversarial examples crafted by the FGSM (Fast Gradient Sign Method) basedattacks on ResNet-50 trained with ImageNet dataset.

Mitigating large adversarial perturbations on X-MAS (X minus Moving Averaged Samples)