Title: Bounded Attacks and Robustness in Image Transform Domains. Abstract: Classical image transformation such as the discrete cosine transform (DCT) and the discrete wavelet transforms (DWTs) provide semantically meaningful representations of images. In this paper we propose a general method for adversarial attacks in such transform domains that, in contrast to prior work, obey the $L^\infty$ constraint in the pixel domain. The key idea is to replace the standard attack based on projections with the barrier method. Experiments with DCT and DWTs produce adversarial examples that are significantly more similar to the original than with prior attacks. Further, through adversarial training we show that robustness against our attacks transfers to robustness against a broad class of common image perturbations.