# Low Photon Count Phase Retrieval Using Deep Learning

arXiv: https://arxiv.org/abs/1806.10029 · HTML: https://mlsanity.com/paper/1806.10029/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jun 2018.

## Built on by (most cited first, 24 of 24)

- [Physics-Informed Computer Vision: A Review and Perspectives](https://mlsanity.com/paper/2305.18035/) (2023)
- [On the use of deep learning for phase recovery](https://mlsanity.com/paper/2308.00942/) (2023)
- [Fourier Imager Network (FIN): A deep neural network for hologram reconstruction with superior external generalization](https://mlsanity.com/paper/2204.10533/) (2022)
- [Deep learning at the edge enables real-time streaming ptychographic imaging](https://mlsanity.com/paper/2209.09408/) (2022)
- [Self-supervised learning of hologram reconstruction using physics consistency](https://mlsanity.com/paper/2209.08288/) (2022)
- [Holographic image reconstruction with phase recovery and autofocusing using recurrent neural networks](https://mlsanity.com/paper/2102.12281/) (2021)
- [eFIN: Enhanced Fourier Imager Network for generalizable autofocusing and pixel super-resolution in holographic imaging](https://mlsanity.com/paper/2301.03162/) (2023)
- [Few-shot Transfer Learning for Holographic Image Reconstruction using a Recurrent Neural Network](https://mlsanity.com/paper/2201.11333/) (2022)
- [Power-law Scaling to Assist with Key Challenges in Artificial Intelligence](https://mlsanity.com/paper/2211.08430/) (2022)
- [Compressive Ptychography using Deep Image and Generative Priors](https://mlsanity.com/paper/2205.02397/) (2022)
- [Physics-assisted Generative Adversarial Network for X-Ray Tomography](https://mlsanity.com/paper/2204.03703/) (2022)
- [Deep-learning real-time phase retrieval of imperfect diffraction patterns from X-ray free-electron lasers](https://mlsanity.com/paper/2409.15784/) (2024)
- [Deep-learning-driven Reliable Single-pixel Imaging with Uncertainty Approximation](https://mlsanity.com/paper/2107.11678/) (2021)
- [Attentional Ptycho-Tomography (APT) for three-dimensional nanoscale X-ray imaging with minimal data acquisition and computation time](https://mlsanity.com/paper/2212.00014/) (2022)
- [What is Wrong with End-to-End Learning for Phase Retrieval?](https://mlsanity.com/paper/2403.15448/) (2024)
- [Investigating the robustness of a learning-based method for quantitative phase retrieval from propagation-based x-ray phase contrast measurements under laboratory conditions](https://mlsanity.com/paper/2211.01372/) (2022)
- [Poisson-Gaussian Holographic Phase Retrieval with Score-based Image Prior](https://mlsanity.com/paper/2305.07712/) (2023)
- [Low-light phase retrieval with implicit generative priors](https://mlsanity.com/paper/2402.17745/) (2024)
- [Joint Segmentation and Image Reconstruction with Error Prediction in Photoacoustic Imaging using Deep Learning](https://mlsanity.com/paper/2407.02653/) (2024)
- [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)
- [3D-2D Neural Nets for Phase Retrieval in Noisy Interferometric Imaging](https://mlsanity.com/paper/2402.06063/) (2024)
- [prNet: Data-Driven Phase Retrieval via Stochastic Refinement](https://mlsanity.com/paper/2507.09608/) (2025)
- [I2I-PR: Deep Iterative Refinement for Phase Retrieval using Image-to-Image Diffusion Models](https://mlsanity.com/paper/2507.09609/) (2025)

## Abstract (arXiv)

Imaging systems' performance at low light intensity is affected by shot noise, which becomes increasingly strong as the power of the light source decreases. In this paper we experimentally demonstrate the use of deep neural networks to recover objects illuminated with weak light and demonstrate better performance than with the classical Gerchberg-Saxton phase retrieval algorithm for equivalent signal over noise ratio. Prior knowledge about the object is implicitly contained in the training data set and feature detection is possible for a signal over noise ratio close to one. We apply this principle to a phase retrieval problem and show successful recovery of the object's most salient features with as little as one photon per detector pixel on average in the illumination beam. We also show that the phase reconstruction is significantly improved by training the neural network with an initial estimate of the object, as opposed as training it with the raw intensity measurement.