# Reliable deep-learning-based phase imaging with uncertainty quantification

## TL;DR

This paper introduces a Bayesian neural network framework for biomedical phase imaging that quantifies prediction uncertainty, enabling reliable, high-resolution imaging and identification of rare biological phenomena.

## Contribution

It presents a novel Bayesian CNN approach that provides uncertainty maps for deep learning-based phase imaging, improving reliability and interpretability of predictions.

## Key findings

- Uncertainty maps correlate with true errors and data imperfections.
- High-quality gigapixel phase images achieved from minimal measurements.
- Low-certainty regions highlight rare biological events.

## Abstract

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.