  Despite the success of convolutional neural networks (CNNs) in many computer
vision and image analysis tasks, they remain vulnerable against so-called
adversarial attacks: Small, crafted perturbations in the input images can lead
to false predictions. A possible defense is to detect adversarial examples. In
this work, we show how analysis in the Fourier domain of input images and
feature maps can be used to distinguish benign test samples from adversarial
images. We propose two novel detection methods: Our first method employs the
magnitude spectrum of the input images to detect an adversarial attack. This
simple and robust classifier can successfully detect adversarial perturbations
of three commonly used attack methods. The second method builds upon the first
and additionally extracts the phase of Fourier coefficients of feature-maps at
different layers of the network. With this extension, we are able to improve
adversarial detection rates compared to state-of-the-art detectors on five
different attack methods.
