# Single Exposure Quantitative Phase Imaging with a Conventional Microscope using Diffusion Models

arXiv: https://arxiv.org/abs/2406.04388 · HTML: https://mlsanity.com/paper/2406.04388/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models.
- Builds on 23 of its 53 references that are in the map.
- First posted on arXiv 6 Jun 2024.

## Placed in

- Diffusion models / [Inverse problems and image restoration](https://mlsanity.com/diffusion/inverse-problems-and-image-restoration/)

## Builds on (most cited first, 23 of 23)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Noise2Noise: Learning Image Restoration without Clean Data](https://mlsanity.com/paper/1803.04189/) (2018)
- [SRDiff: Single Image Super-Resolution with Diffusion Probabilistic Models](https://mlsanity.com/paper/2104.14951/) (2021)
- [Score-based diffusion models for accelerated MRI](https://mlsanity.com/paper/2110.05243/) (2021)
- [Diffusion Probabilistic Modeling for Video Generation](https://mlsanity.com/paper/2203.09481/) (2022)
- [Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localization](https://mlsanity.com/paper/2308.03686/) (2023)
- [Diffusion Models for Image Restoration and Enhancement: A Comprehensive Survey](https://mlsanity.com/paper/2308.09388/) (2023)
- [prDeep: Robust Phase Retrieval with a Flexible Deep Network](https://mlsanity.com/paper/1803.00212/) (2018)
- [PhaseStain: Digital staining of label-free quantitative phase microscopy images using deep learning](https://mlsanity.com/paper/1807.07701/) (2018)
- [How Much is Enough? A Study on Diffusion Times in Score-based Generative Models](https://mlsanity.com/paper/2206.05173/) (2022)
- [Physics-driven Synthetic Data Learning for Biomedical Magnetic Resonance](https://mlsanity.com/paper/2203.11178/) (2022)
- [On the use of deep learning for phase recovery](https://mlsanity.com/paper/2308.00942/) (2023)
- [PhaseGAN: A deep-learning phase-retrieval approach for unpaired datasets](https://mlsanity.com/paper/2011.08660/) (2020)
- [Image Harmonization Dataset iHarmony4: HCOCO, HAdobe5k, HFlickr, and Hday2night](https://mlsanity.com/paper/1908.10526/) (2019)
- [Conditional Variational Diffusion Models](https://mlsanity.com/paper/2312.02246/) (2023)

## Built on by (most cited first, 1 of 1)

- [Diffusion Models to Enhance the Resolution of Microscopy Images: A Tutorial](https://mlsanity.com/paper/2409.16488/) (2024)

## Abstract (arXiv)

Phase imaging is gaining importance due to its applications in fields like biomedical imaging and material characterization. In biomedical applications, it can provide quantitative information missing in label-free microscopy modalities. One of the most prominent methods in phase quantification is the Transport-of-Intensity Equation (TIE). TIE often requires multiple acquisitions at different defocus distances, which is not always feasible in a clinical setting. To address this issue, we propose to use chromatic aberrations to induce the required through-focus images with a single exposure, effectively generating a through-focus stack. Since the defocus distance induced by the aberrations is small, conventional TIE solvers are insufficient to address the resulting artifacts. We propose Zero-Mean Diffusion, a modified version of diffusion models designed for quantitative image prediction, and train it with synthetic data to ensure robust phase retrieval. Our contributions offer an alternative TIE approach that leverages chromatic aberrations, achieving accurate single-exposure phase measurement with white light and thus improving the efficiency of phase imaging. Moreover, we present a new class of diffusion models that are well-suited for quantitative data and have a sound theoretical basis. To validate our approach, we employ a widespread brightfield microscope equipped with a commercially available color camera. We apply our model to clinical microscopy of patients' urine, obtaining accurate phase measurements.