Adversarial attacks for machine learning denoisers and how to resist them

Adversarial attacks rely on the instability phenomenon appearing in general for all inverse problems, e.g., image classification and reconstruction, independently of the computational scheme or method used to solve the prob- lem. We mathematically prove and empirically show that machine learning denoisers (MLD) are not excluded. That is to prove the existence of adversarial attacks given by noise patterns making the MLD run into instability, i.e., the MLD increases the noise instead of decreasing it. We further demonstrate that adversarial retraining or classic filtering do not provide an exit strategy for this dilemma. Instead, we show that adversarial attacks can be inferred by polynomial regression. Removing the underlying inferred polynomial distribution from the total noise distribution delivers an efficient technique yielding robust MLDs that make consistent computer vision tasks such as image segmentation or classification more reliable.