mlsanityData to 14 Oct 2026

Complex-valued Retrievals From Noisy Images Using Diffusion Models

arXiv 2212.03235 ↗First posted 6 Dec 2022cs.CV cs.AIcited by 3

On the map: Diffusion models → Inverse problems and image restoration

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.

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.

Builds on

27 of 59 references.

Closest ancestors · 4

Same direction, newest first

  1. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep
  2. 2022Improving Diffusion Models for Inverse Problems using Manifold Constraints2 Jun
  3. 2022Denoising Diffusion Restoration Models27 Jan
  4. 2021Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contraction9 Dec

Other references · 23

  1. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  2. 2016Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoisingcited by 1,358
  3. 2020Improved Techniques for Training Score-Based Generative Modelscited by 1,043
  4. 2021ILVR: Conditioning Method for Denoising Diffusion Probabilistic Modelscited by 635
  5. 2017The Perception-Distortion Tradeoffcited by 587
  6. 2021Solving Inverse Problems in Medical Imaging with Score-Based Generative Modelscited by 521
  7. 2018Noise2Void - Learning Denoising from Single Noisy Imagescited by 364
  8. 2016The Little Engine that Could: Regularization by Denoising (RED)cited by 307
  9. 2015Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restorationcited by 195
  10. 2021SNIPS: Solving Noisy Inverse Problems Stochasticallycited by 191
  11. 2021Neighbor2Neighbor: Self-Supervised Denoising from Single Noisy Imagescited by 173
  12. 2018Non-Local Recurrent Network for Image Restorationcited by 160
11 more
  1. 2017Burst Denoising with Kernel Prediction Networkscited by 157
  2. 2018A Poisson-Gaussian Denoising Dataset with Real Fluorescence Microscopy Imagescited by 71
  3. 2018prDeep: Robust Phase Retrieval with a Flexible Deep Networkcited by 47
  4. 2021Stochastic Image Denoising by Sampling from the Posterior Distributioncited by 45
  5. 2021FBI-Denoiser: Fast Blind Image Denoiser for Poisson-Gaussian Noisecited by 22
  6. 2015Experimental robustness of Fourier Ptychography phase retrieval algorithmscited by 14
  7. 2020Self-Supervised Poisson-Gaussian Denoisingcited by 9
  8. 2020Solving Phase Retrieval with a Learned Referencecited by 8
  9. 2020DeepPhaseCut: Deep Relaxation in Phase for Unsupervised Fourier Phase Retrievalcited by 8
  10. 2018Efficient illumination angle self-calibration in Fourier ptychographycited by 6
  11. 2022LWGNet: Learned Wirtinger Gradients for Fourier Ptychographic Phase Retrievalcited by 2

Built on by

Cited by year

Citing papers per year: 2023: 1; 2024: 1; 2025: 1.

3 papers.

  1. 2023Tell Me What You See: Text-Guided Real-World Image Denoisingcited by 2
  2. 2024Fast and Robust Phase Retrieval via Deep Expectation-Consistent Approximationcited by 2
  3. 2025NnD: Diffusion-based Generation of Physically-Nonnegative Objectscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2024Denoising diffusion models for high-resolution microscopy image restoration
  2. 2025Posterior Sampling by Combining Diffusion Models with Annealed Langevin Dynamics
  3. 2024Denoising Diffusion Restoration Tackles Forward and Inverse Problems for the Laplace Operator
  4. 2024Learning Diffusion Model from Noisy Measurement using Principled Expectation-Maximization Method
  5. 2026Mixed Poisson diffusion models and application to posterior sampling
  6. 2025Computationally Efficient Diffusion Models in Medical Imaging: A Comprehensive Review
  7. 2024Diffusion Models to Enhance the Resolution of Microscopy Images: A Tutorial
  8. 2024General Intelligent Imaging and Uncertainty Quantification by Deterministic Diffusion Model