Uncertainty estimation is critical for numerous applications of deep neural networks and draws growing attention from researchers. Here, we demonstrate an uncertainty quantification approach for deep neural networks used in inverse problems based on cycle consistency. We build forward-backward cycles using the physical forward model available and a trained deep neural network solving the inverse problem at hand, and accordingly derive uncertainty estimators through regression analysis on the consistency of these forward-backward cycles. We theoretically analyze cycle consistency metrics and derive their relationship with respect to uncertainty, bias, and robustness of the neural network inference. To demonstrate the effectiveness of these cycle consistency-based uncertainty estimators, we classified corrupted and out-of-distribution input image data using some of the widely used image deblurring and super-resolution neural networks as testbeds. The blind testing of our method outperformed other models in identifying unseen input data corruption and distribution shifts. This work provides a simple-to-implement and rapid uncertainty quantification method that can be universally applied to various neural networks used for solving inverse problems.

翻译：不确定性估计对于深度神经网络的众多应用至关重要，并日益受到研究者的关注。本文基于循环一致性，提出了一种适用于逆问题中深度神经网络的不确定性量化方法。我们利用可用的物理正向模型和用于求解给定逆问题的已训练深度神经网络构建前向-反向循环，并通过对这些前向-反向循环的一致性进行回归分析，推导出相应的不确定性估计量。我们从理论上分析了循环一致性度量指标，并推导了它们与神经网络推理的不确定性、偏差及鲁棒性之间的关系。为了验证这些基于循环一致性的不确定性估计量的有效性，我们以一些广泛使用的图像去模糊和超分辨率神经网络作为测试平台，对受污染的输入图像数据和分布外输入图像数据进行了分类。盲测结果表明，该方法在识别未见过的输入数据损坏和分布偏移方面优于其他模型。本文提供了一种易于实现且快速的不确定性量化方法，可普适于各种用于求解逆问题的神经网络。