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.

翻译：我们研究了用于图像逆问题求解的确定性方法的行为。这些方法通常设计用于实现两个目标：(1) 达到高感知质量，和(2) 生成与测量一致的复原结果。我们严格证明，无论涉及何种退化类型，预测器越能满足这两个要求，其Lipschitz常数就必须越大。特别地，要趋近于完美的感知质量和完全的一致性，模型的Lipschitz常数必须趋向于无穷大。这意味着此类方法必然更容易受到对抗攻击。我们在单图像超分辨率算法上验证了我们的理论，同时考虑了含噪和无噪设置。我们还展示了如何利用这种不良行为来探索后验分布，从而使确定性模型能够模仿随机方法。