  The vulnerability of convolutional neural networks (CNNs) to image
perturbations such as common corruptions and adversarial perturbations has
recently been investigated from the perspective of frequency. In this study, we
investigate the effect of the amplitude and phase spectra of adversarial images
on the robustness of CNN classifiers. Extensive experiments revealed that the
images generated by combining the amplitude spectrum of adversarial images and
the phase spectrum of clean images accommodates moderate and general
perturbations, and training with these images equips a CNN classifier with more
general robustness, performing well under both common corruptions and
adversarial perturbations. We also found that two types of overfitting
(catastrophic overfitting and robust overfitting) can be circumvented by the
aforementioned spectrum recombination. We believe that these results contribute
to the understanding and the training of truly robust classifiers.
