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Uncertainty estimation is critical for numerous applications of deep neuralnetworks and draws growing attention from researchers. Here, we demonstrate anuncertainty quantification approach for deep neural networks used in inverseproblems based on cycle consistency. We build forward-backward cycles using thephysical forward model available and a trained deep neural network solving theinverse problem at hand, and accordingly derive uncertainty estimators throughregression analysis on the consistency of these forward-backward cycles. Wetheoretically analyze cycle consistency metrics and derive their relationshipwith respect to uncertainty, bias, and robustness of the neural networkinference. To demonstrate the effectiveness of these cycle consistency-baseduncertainty estimators, we classified corrupted and out-of-distribution inputimage data using some of the widely used image deblurring and super-resolutionneural networks as testbeds. The blind testing of our method outperformed othermodels in identifying unseen input data corruption and distribution shifts.This work provides a simple-to-implement and rapid uncertainty quantificationmethod that can be universally applied to various neural networks used forsolving inverse problems.

Cycle Consistency-based Uncertainty Quantification of Neural Networks in Inverse Imaging Problems