  Image restoration algorithms are typically evaluated by some distortion
measure (e.g. PSNR, SSIM, IFC, VIF) or by human opinion scores that quantify
perceived perceptual quality. In this paper, we prove mathematically that
distortion and perceptual quality are at odds with each other. Specifically, we
study the optimal probability for correctly discriminating the outputs of an
image restoration algorithm from real images. We show that as the mean
distortion decreases, this probability must increase (indicating worse
perceptual quality). As opposed to the common belief, this result holds true
for any distortion measure, and is not only a problem of the PSNR or SSIM
criteria. We also show that generative-adversarial-nets (GANs) provide a
principled way to approach the perception-distortion bound. This constitutes
theoretical support to their observed success in low-level vision tasks. Based
on our analysis, we propose a new methodology for evaluating image restoration
methods, and use it to perform an extensive comparison between recent
super-resolution algorithms.
