  Emerging deep-learning (DL)-based techniques have significant potential to
revolutionize biomedical imaging. However, one outstanding challenge is the
lack of reliability assessment in the DL predictions, whose errors are commonly
revealed only in hindsight. Here, we propose a new Bayesian convolutional
neural network (BNN)-based framework that overcomes this issue by quantifying
the uncertainty of DL predictions. Foremost, we show that BNN-predicted
uncertainty maps provide surrogate estimates of the true error from the network
model and measurement itself. The uncertainty maps characterize imperfections
often unknown in real-world applications, such as noise, model error,
incomplete training data, and out-of-distribution testing data. Quantifying
this uncertainty provides a per-pixel estimate of the confidence level of the
DL prediction as well as the quality of the model and dataset. We demonstrate
this framework in the application of large space-bandwidth product phase
imaging using a physics-guided coded illumination scheme. From only five
multiplexed illumination measurements, our BNN predicts gigapixel phase images
in both static and dynamic biological samples with quantitative credibility
assessment. Furthermore, we show that low-certainty regions can identify
spatially and temporally rare biological phenomena. We believe our uncertainty
learning framework is widely applicable to many DL-based biomedical imaging
techniques for assessing the reliability of DL predictions.
