# Complex-valued Retrievals From Noisy Images Using Diffusion Models

arXiv: https://arxiv.org/abs/2212.03235 · HTML: https://mlsanity.com/paper/2212.03235/

## Key facts

- Cited by 3 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 27 of its 59 references that are in the map.
- First posted on arXiv 6 Dec 2022.

## Placed in

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

## Builds on (most cited first, 27 of 27)

- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [ILVR: Conditioning Method for Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2108.02938/) (2021)
- [The Perception-Distortion Tradeoff](https://mlsanity.com/paper/1711.06077/) (2017)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [Noise2Void - Learning Denoising from Single Noisy Images](https://mlsanity.com/paper/1811.10980/) (2018)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contraction](https://mlsanity.com/paper/2112.05146/) (2021)
- [Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restoration](https://mlsanity.com/paper/1508.02848/) (2015)
- [SNIPS: Solving Noisy Inverse Problems Stochastically](https://mlsanity.com/paper/2105.14951/) (2021)
- [Neighbor2Neighbor: Self-Supervised Denoising from Single Noisy Images](https://mlsanity.com/paper/2101.02824/) (2021)
- [Non-Local Recurrent Network for Image Restoration](https://mlsanity.com/paper/1806.02919/) (2018)
- [Burst Denoising with Kernel Prediction Networks](https://mlsanity.com/paper/1712.02327/) (2017)
- [A Poisson-Gaussian Denoising Dataset with Real Fluorescence Microscopy Images](https://mlsanity.com/paper/1812.10366/) (2018)
- [prDeep: Robust Phase Retrieval with a Flexible Deep Network](https://mlsanity.com/paper/1803.00212/) (2018)
- [Stochastic Image Denoising by Sampling from the Posterior Distribution](https://mlsanity.com/paper/2101.09552/) (2021)
- [FBI-Denoiser: Fast Blind Image Denoiser for Poisson-Gaussian Noise](https://mlsanity.com/paper/2105.10967/) (2021)
- [Experimental robustness of Fourier Ptychography phase retrieval algorithms](https://mlsanity.com/paper/1511.02986/) (2015)
- [Self-Supervised Poisson-Gaussian Denoising](https://mlsanity.com/paper/2002.09558/) (2020)
- [Solving Phase Retrieval with a Learned Reference](https://mlsanity.com/paper/2007.14621/) (2020)
- [DeepPhaseCut: Deep Relaxation in Phase for Unsupervised Fourier Phase Retrieval](https://mlsanity.com/paper/2011.10475/) (2020)
- [Efficient illumination angle self-calibration in Fourier ptychography](https://mlsanity.com/paper/1804.03299/) (2018)
- [LWGNet: Learned Wirtinger Gradients for Fourier Ptychographic Phase Retrieval](https://mlsanity.com/paper/2208.04283/) (2022)

## Built on by (most cited first, 3 of 3)

- [Tell Me What You See: Text-Guided Real-World Image Denoising](https://mlsanity.com/paper/2312.10191/) (2023)
- [Fast and Robust Phase Retrieval via Deep Expectation-Consistent Approximation](https://mlsanity.com/paper/2407.09687/) (2024)
- [NnD: Diffusion-based Generation of Physically-Nonnegative Objects](https://mlsanity.com/paper/2506.10112/) (2025)

## Abstract (arXiv)

In diverse microscopy modalities, sensors measure only real-valued intensities. Additionally, the sensor readouts are affected by Poissonian-distributed photon noise. Traditional restoration algorithms typically aim to minimize the mean squared error (MSE) between the original and recovered images. This often leads to blurry outcomes with poor perceptual quality. Recently, deep diffusion models (DDMs) have proven to be highly capable of sampling images from the a-posteriori probability of the sought variables, resulting in visually pleasing high-quality images. These models have mostly been suggested for real-valued images suffering from Gaussian noise. In this study, we generalize annealed Langevin Dynamics, a type of DDM, to tackle the fundamental challenges in optical imaging of complex-valued objects (and real images) affected by Poisson noise. We apply our algorithm to various optical scenarios, such as Fourier Ptychography, Phase Retrieval, and Poisson denoising. Our algorithm is evaluated on simulations and biological empirical data.