Source-linked AI summary
Reliable deep-learning-based phase imaging with uncertainty quantification
Yujia Xue, Shiyi Cheng, Yunzhe Li, Lei Tian
TL;DR
Deep-learning phase predictions are difficult to evaluate reliably when ground truth is unavailable. The paper develops a Bayesian convolutional neural-network framework combining physics-guided five-measurement phase imaging with uncertainty quantification, and reports uncertainty maps that track prediction error and support quantitative reliability assessment.
Problem
Deep-learning prediction errors are difficult to evaluate without known ground truth, limiting reliability assessment in biomedical imaging.
Method
The framework combines physics-guided large-SBP phase imaging using five coded measurements with a Bayesian convolutional neural network modeling model and data uncertainty.
Results
The predicted uncertainty maps generally match absolute-error maps, with uncertainty values about 1/3 of the absolute error in the reported experiments.
Takeaways & Limitations
BNN uncertainty maps provide per-pixel reliability information for assessing phase predictions and imperfections in the model, measurements, and data.
Takeaways & Limitations
Reliability analysis uses an unknown ground-truth mean approximated by a noisy sFPM reconstruction, so measured accuracy depends on that reconstruction quality.
Abstract
from arXiv · showhide
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.
1 Introduction
The paper combines physics-guided coded illumination with Bayesian deep learning to perform large-SBP phase imaging while quantifying prediction reliability. Its framework uses five measurements and uncertainty analysis to assess model, data, and experimental limitations.
- Motivation: Traditional imaging faces a fundamental trade-off among field of view, resolution, and acquisition speed.The associated space-bandwidth-product constraint becomes more severe when resolution enhancement or field-of-view expansion requires multiple measurements.
- Measurement strategy: The proposed physics-guided approach combines asymmetric and oblique illumination to encode large-SBP phase information with only five coded measurements.It uses differential phase contrast, synthetic-aperture, and Fourier-ptychographic principles to introduce high-frequency information while avoiding quadratic measurement growth.
- Uncertainty learning: A Bayesian convolutional neural network addresses the ill-posed inverse problem and quantifies model and data uncertainties.Model uncertainty reflects variability across trained networks, while data uncertainty captures imperfections such as noise, incomplete training data, and out-of-distribution testing data.
- Reliability assessment: The framework relates BNN outputs to credibility, credible intervals, and reliability diagrams for systematic assessment of prediction reliability.This statistical procedure is intended to evaluate both the phase-retrieval technique and its uncertainty estimates.
- Experimental validation: Experiments demonstrate 5× resolution enhancement on one platform and 4× improvement on static and dynamic biological data from another.These experiments also evaluate robustness to common experimental factors using BNN-predicted uncertainties.
2 Method
The method combines five-pattern multiplexed illumination with a Bayesian neural network to recover high-resolution phase while estimating data and model uncertainty. Statistical analysis converts ensemble predictions into pixel-wise uncertainty and calibrated reliability measures.
- Multiplexed illumination: Five asymmetric illumination patterns combine DPC and FPM principles to provide complete brightfield Fourier coverage and extend coverage through darkfield measurements.Two brightfield patterns use two axes of asymmetry, while three darkfield patterns use three axes to extend coverage by the illumination and objective numerical apertures.
- Bayesian uncertainty learning: The BNN models both network-weight and output randomness to quantify model and data uncertainty in phase predictions.The predictive distribution marginalizes over possible network weights, while pixel-wise output standard deviations model data uncertainty.
- Data uncertainty: Spatially varying standard deviations account for inhomogeneous noise and shift-variant model errors, while the uncertainty-regularized likelihood learns uncertainty without ground-truth means.The loss combines a residual term normalized by pixel-wise standard deviation with a data-uncertainty regularization term.
- Prediction and uncertainty maps: During testing, the BNN produces ensemble mean and standard-deviation maps that are statistically combined into phase, data-uncertainty, and model-uncertainty maps.The network estimates both the mean and standard deviation for each testing input, and pixel-wise variance provides an overall uncertainty measure.
- Model uncertainty: Deep Ensembles quantify model uncertainty by training eight networks under the same conditions and applying the ensemble procedures to their predictions.The ensemble captures variability arising from stochastic neural-network training.
- Reliability assessment: Reliability diagrams compare empirical accuracy with predicted credibility to assess whether the uncertainty metrics are calibrated.Well-calibrated metrics produce credibility values similar to accuracy, represented by a diagonal reliability diagram.
3 Results
The results show that the physics-guided BNN produces scalable high-resolution phase predictions while its uncertainty and credibility maps track prediction errors, data incompleteness, and rare biological events.
- Scalable phase imaging: Five multiplexed measurements support scalable phase imaging across multiple samples, microscope setups, and final resolutions.Experiments used five cell types, two microscope setups, and three achieved resolutions.
- Scalable phase imaging: The BNN provides high-quality phase predictions without degrading performance relative to the CNN approach.The predictions are evaluated against sFPM phase and pixel-wise absolute error maps.
- Scalable phase imaging: Compared with model-based methods using the same measurements, linear DPC has limited resolution while mFPM produces high-frequency artifacts.These comparisons motivate the DL method for the ill-posed phase-retrieval problem.
- Uncertainty assessment: Uncertainty maps generally match absolute error maps, with predicted uncertainty about one-third of absolute error under the Laplace 95% credible-interval approximation.Data uncertainty dominates model uncertainty, indicating incomplete training data as the main observed error source.
- Uncertainty assessment: The BNN detects out-of-distribution measurements from different cell types, with uncertainty remaining indicative of absolute error despite slight prediction degradation.Distinct morphology can alter intensity measurements beyond the statistical variations represented in training data.
- Large-SBP prediction: Full-FOV model uncertainty stays low except near boundaries, where severe experimental errors increase variation across network predictions.The low uncertainty across most of the FOV supports robust high-resolution phase prediction there.
- Large-SBP prediction: Training on only a 0.4 × 0.4mm2 central region of a 3.5 × 4.2mm2 FOV creates out-of-distribution conditions toward larger field angles.Aberration, illumination-angle mis-calibration, and background nonuniformity increase away from the center.
- Large-SBP prediction: Adding training examples that cover other FOV aberrations and angle mis-calibration can reduce data uncertainty and improve prediction credibility.The uncertainty therefore provides feedback for improving the DL data pipeline.
4 Conclusion
The paper presents a physics-guided DL framework for large-SBP phase imaging that combines high-resolution inference with uncertainty-based reliability assessment.
- The framework performs high-resolution phase inference across a wide FOV using only five asymmetric illumination coded intensity measurements.
- The BNN learns the underlying physical model, robustly solves phase retrieval, and generalizes across different samples.
- Uncertainty quantification assesses prediction reliability, illumination-coding robustness, experimental errors, incomplete training data, and out-of-distribution testing errors.
- Credibility maps help identify spatially and temporally rare biological phenomena and characterize temporal decorrelation in dynamic processes.
Funding Information
The work was supported by the National Science Foundation and the National Institutes of Health.
- Funding was provided by the National Science Foundation (1813848) and National Institute of Health (R21GM128020).
Testing cell type
The figures examine phase-retrieval robustness across sample types, wide-field conditions, and reliability configurations using prediction and uncertainty maps.
- BNN predictions remain robust across variations in sample type, while uncertainty maps identify potential phase-prediction errors.
- Full-FOV phase prediction reaches 0.51 NA resolution across a 4× FOV, with data uncertainty identifying peripheral out-of-distribution regions.
- Model uncertainty stays low across most of the FOV but increases near the boundary, where prediction robustness is reduced.
- Less credible regions coincide with out-of-distribution data containing phase clipping and wrapping artifacts.
- Reliability diagrams show slight over-confidence for cases (i–ii) and better calibration for cases (iii–v), while predicted 95% credible intervals correlate with true absolute error.
- Time-series predictions quantify credibility across the whole FOV, cell region, and background to assess temporal decorrelation.