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.

我们研究了确定性成像逆问题求解方法的行为，证明了为了实现高感知质量和与测量一致的重建，越好的预测器的利普希茨常数必须越大，这意味着这种方法对敌对攻击更加敏感。我们在单图像超分辨率算法上展示了我们的理论，并展示了如何利用这种不希望的行为来探索后验分布，从而使确定性模型模仿随机方法。

确定性图像恢复中的感知稳健性权衡