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

arXiv: https://arxiv.org/abs/1901.02038 · HTML: https://mlsanity.com/paper/1901.02038/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jan 2019.

## Built on by (most cited first, 26 of 26)

- [On the use of deep learning for phase recovery](https://mlsanity.com/paper/2308.00942/) (2023)
- [Uncertainty Quantification for Deep Unrolling-Based Computational Imaging](https://mlsanity.com/paper/2207.00698/) (2022)
- [Task-Driven Uncertainty Quantification in Inverse Problems via Conformal Prediction](https://mlsanity.com/paper/2405.18527/) (2024)
- [Compressive Ptychography using Deep Image and Generative Priors](https://mlsanity.com/paper/2205.02397/) (2022)
- [Conformalized Generative Bayesian Imaging: An Uncertainty Quantification Framework for Computational Imaging](https://mlsanity.com/paper/2504.07696/) (2025)
- [Uncertainty quantification for ptychography using normalizing flows](https://mlsanity.com/paper/2111.00745/) (2021)
- [Cycle Consistency-based Uncertainty Quantification of Neural Networks in Inverse Imaging Problems](https://mlsanity.com/paper/2305.12852/) (2023)
- [Physical model simulator-trained neural network for computational 3D phase imaging of multiple-scattering samples](https://mlsanity.com/paper/2103.15795/) (2021)
- [Block Modulating Video Compression: An Ultra Low Complexity Image Compression Encoder for Resource Limited Platforms](https://mlsanity.com/paper/2205.03677/) (2022)
- [Uncertainty-aware Grounded Action Transformation towards Sim-to-Real Transfer for Traffic Signal Control](https://mlsanity.com/paper/2307.12388/) (2023)
- [Learned, uncertainty-driven adaptive acquisition for photon-efficient scanning microscopy](https://mlsanity.com/paper/2310.16102/) (2023)
- [Neural Network-Based Processing and Reconstruction of Compromised Biophotonic Image Data](https://mlsanity.com/paper/2403.14324/) (2024)
- [Deep-learning-driven Reliable Single-pixel Imaging with Uncertainty Approximation](https://mlsanity.com/paper/2107.11678/) (2021)
- [Local Conditional Neural Fields for Versatile and Generalizable Large-Scale Reconstructions in Computational Imaging](https://mlsanity.com/paper/2307.06207/) (2023)
- [Conformal Bounds on Full-Reference Image Quality for Imaging Inverse Problems](https://mlsanity.com/paper/2505.09528/) (2025)
- [Differentiable Microscopy Designs an All Optical Phase Retrieval Microscope](https://mlsanity.com/paper/2203.14944/) (2022)
- [Density Regression and Uncertainty Quantification with Bayesian Deep Noise Neural Networks](https://mlsanity.com/paper/2206.05643/) (2022)
- [Deep learning phase recovery: data-driven, physics-driven, or combining both?](https://mlsanity.com/paper/2404.01360/) (2024)
- [Joint Segmentation and Image Reconstruction with Error Prediction in Photoacoustic Imaging using Deep Learning](https://mlsanity.com/paper/2407.02653/) (2024)
- [CameraVDP: Perceptual Display Assessment with Uncertainty Estimation via Camera and Visual Difference Prediction](https://mlsanity.com/paper/2509.08947/) (2025)
- [ShuffleFlow: Scalable Posterior Inference for Bayesian Inverse Imaging](https://mlsanity.com/paper/2606.21099/) (2026)
- [Blaschke Product Neural Networks (BPNN): A Physics-Infused Neural Network for Phase Retrieval of Meromorphic Functions](https://mlsanity.com/paper/2111.13311/) (2021)
- [A Deep Generative Approach to Oversampling in Ptychography](https://mlsanity.com/paper/2207.14392/) (2022)
- [General Intelligent Imaging and Uncertainty Quantification by Deterministic Diffusion Model](https://mlsanity.com/paper/2408.13061/) (2024)
- [QUTCC: Quantile Uncertainty Training and Conformal Calibration for Imaging Inverse Problems](https://mlsanity.com/paper/2507.14760/) (2025)
- [Self-supervised physics-informed generative networks for phase retrieval from a single X-ray hologram](https://mlsanity.com/paper/2508.15530/) (2025)

## Abstract (arXiv)

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.