确定性图像复原中的感知-鲁棒性权衡
The Perception-Robustness Tradeoff in Deterministic Image Restoration
AI总结：
本文证明确定性图像复原方法在追求高感知质量与测量一致性的同时必然导致Lipschitz常数增大、对抗鲁棒性下降，并在超分辨率任务上验证该理论，进一步利用此特性使确定性模型模仿随机方法。
摘要：
我们研究用于求解成像中逆问题的确定性方法的行为。这些方法通常被设计来实现两个目标：（1）获得高感知质量，以及（2）生成与测量结果一致的重建。我们给出一个严格的证明：一个预测器越能满足这两个要求，其Lipschitz常数就必须越大，无论所涉及的退化性质如何。特别地，要接近完美的感知质量和完美的一致性，模型的Lipschitz常数必须趋于无穷大。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，同时考虑了有噪声和无噪声两种设置。我们还展示了如何利用这种不希望出现的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。
英文摘要：
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.
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