The Perception-Robustness Tradeoff in Deterministic Image Restoration
Guy Ohayon Tomer Michaeli Michael Elad
We study the behavior of deterministic methods for solving inverse problems
in imaging. These methods are commonly designed to achieve two goals: (1)
attaining high perceptual quality, and (2) generating reconstructions that are
consistent with the measurements. We provide a rigorous proof that the better a
predictor satisfies these two requirements, the larger its Lipschitz constant
must be, regardless of the nature of the degradation involved. In particular,
to approach perfect perceptual quality and perfect consistency, the Lipschitz
constant of the model must grow to infinity. This implies that such methods are
necessarily more susceptible to adversarial attacks. We demonstrate our theory
on single image super-resolution algorithms, addressing both noisy and
noiseless settings. We also show how this undesired behavior can be leveraged
to explore the posterior distribution, thereby allowing the deterministic model
to imitate stochastic methods.