May denoising remove structures? How to reconstruct invariances of CT denoising algorithms

Many methods have been developed to reduce radiation dose in computed tomography (CT) scans without sacrificing image quality. Recently, deep learning-based methods have shown promising results on the task of CT image denoising. However, they remain difficult to interpret, and thus safety concerns have been raised. In this work we develop a method to reconstruct the invariances of arbitrary denoising methods with an approach inspired by the optimization schemes commonly used to generate adversarial examples. We apply our method to one proof-of-principle algorithm as well as to two previously proposed denoising networks and show that it can successfully reconstruct their invariances.