# On the use of deep learning for phase recovery

arXiv: https://arxiv.org/abs/2308.00942 · HTML: https://mlsanity.com/paper/2308.00942/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Builds on 89 of its 377 references that are in the map.
- First posted on arXiv 2 Aug 2023.

## Builds on (most cited first, 30 of 89)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Image Super-Resolution Using Deep Convolutional Networks](https://mlsanity.com/paper/1501.00092/) (2014)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Multi-Stage Progressive Image Restoration](https://mlsanity.com/paper/2102.02808/) (2021)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [FFDNet: Toward a Fast and Flexible Solution for CNN based Image Denoising](https://mlsanity.com/paper/1710.04026/) (2017)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [All-Optical Machine Learning Using Diffractive Deep Neural Networks](https://mlsanity.com/paper/1804.08711/) (2018)
- [Phase Retrieval via Wirtinger Flow: Theory and Algorithms](https://mlsanity.com/paper/1407.1065/) (2014)
- [Deep Decoder: Concise Image Representations from Untrained Non-convolutional Networks](https://mlsanity.com/paper/1810.03982/) (2018)
- [Photonics for artificial intelligence and neuromorphic computing](https://mlsanity.com/paper/2011.00111/) (2020)
- [Phase Retrieval Under a Generative Prior](https://mlsanity.com/paper/1807.04261/) (2018)
- [Phase recovery and holographic image reconstruction using deep learning in neural networks](https://mlsanity.com/paper/1705.04286/) (2017)
- [prDeep: Robust Phase Retrieval with a Flexible Deep Network](https://mlsanity.com/paper/1803.00212/) (2018)
- [Lensless computational imaging through deep learning](https://mlsanity.com/paper/1702.08516/) (2017)
- [PhaseStain: Digital staining of label-free quantitative phase microscopy images using deep learning](https://mlsanity.com/paper/1807.07701/) (2018)
- [Algorithmic Guarantees for Inverse Imaging with Untrained Network Priors](https://mlsanity.com/paper/1906.08763/) (2019)
- [Solving Systems of Random Quadratic Equations via Truncated Amplitude Flow](https://mlsanity.com/paper/1605.08285/) (2016)
- [Reliable deep-learning-based phase imaging with uncertainty quantification](https://mlsanity.com/paper/1901.02038/) (2019)
- [Low Photon Count Phase Retrieval Using Deep Learning](https://mlsanity.com/paper/1806.10029/) (2018)
- [Deep Phase Decoder: Self-calibrating phase microscopy with an untrained deep neural network](https://mlsanity.com/paper/2001.09803/) (2020)
- [Shape Inpainting using 3D Generative Adversarial Network and Recurrent Convolutional Networks](https://mlsanity.com/paper/1711.06375/) (2017)
- [Diffractive all-optical computing for quantitative phase imaging](https://mlsanity.com/paper/2201.08964/) (2022)
- [To image, or not to image: Class-specific diffractive cameras with all-optical erasure of undesired objects](https://mlsanity.com/paper/2205.13122/) (2022)

## Built on by (most cited first, 20 of 20)

- [All-optical complex field imaging using diffractive processors](https://mlsanity.com/paper/2401.16779/) (2024)
- [DDRM-PR: Fourier Phase Retrieval using Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2501.03030/) (2025)
- [Low-light phase retrieval with implicit generative priors](https://mlsanity.com/paper/2402.17745/) (2024)
- [Single Exposure Quantitative Phase Imaging with a Conventional Microscope using Diffusion Models](https://mlsanity.com/paper/2406.04388/) (2024)
- [Single-shot reconstruction of three-dimensional morphology of biological cells in digital holographic microscopy using a physics-driven neural network](https://mlsanity.com/paper/2409.20013/) (2024)
- [Towards generalizable deep ptychography neural networks](https://mlsanity.com/paper/2509.25104/) (2025)
- [RamPINN: Recovering Raman Spectra From Coherent Anti-Stokes Spectra Using Embedded Physics](https://mlsanity.com/paper/2510.06020/) (2025)
- [Circular Phase Representation and Geometry-Aware Optimization for Ptychographic Image Reconstruction](https://mlsanity.com/paper/2604.26664/) (2026)
- [Single-shot Phase Retrieval from a Fractional Fourier Transform Perspective](https://mlsanity.com/paper/2311.10950/) (2023)
- [Res-U2Net: Untrained Deep Learning for Phase Retrieval and Image Reconstruction](https://mlsanity.com/paper/2404.06657/) (2024)
- [Artificial intelligence inspired freeform optics design: a review](https://mlsanity.com/paper/2410.03554/) (2024)
- [Single-Shot Phase Diversity Wavefront Sensing in Deep Turbulence via Metasurface Optics](https://mlsanity.com/paper/2410.18789/) (2024)
- [GUSLO: General and Unified Structured Light Optimization](https://mlsanity.com/paper/2501.14659/) (2025)
- [Towards Robust and Generalizable Gerchberg Saxton based Physics Inspired Neural Networks for Computer Generated Holography: A Sensitivity Analysis Framework](https://mlsanity.com/paper/2505.00220/) (2025)
- [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)
- [Self-supervised physics-informed generative networks for phase retrieval from a single X-ray hologram](https://mlsanity.com/paper/2508.15530/) (2025)
- [Pupil Design for Computational Wavefront Estimation](https://mlsanity.com/paper/2604.00225/) (2026)
- [Contrast-invariant deep ptychography neural networks](https://mlsanity.com/paper/2608.02869/) (2026)
- [Real-Time Atomic-Resolution Electron Phase Imaging without Probe Calibration via Ptychography-Supervised Learning](https://mlsanity.com/paper/2609.25684/) (2026)

## Abstract (arXiv)

Phase recovery (PR) refers to calculating the phase of the light field from its intensity measurements. As exemplified from quantitative phase imaging and coherent diffraction imaging to adaptive optics, PR is essential for reconstructing the refractive index distribution or topography of an object and correcting the aberration of an imaging system. In recent years, deep learning (DL), often implemented through deep neural networks, has provided unprecedented support for computational imaging, leading to more efficient solutions for various PR problems. In this review, we first briefly introduce conventional methods for PR. Then, we review how DL provides support for PR from the following three stages, namely, pre-processing, in-processing, and post-processing. We also review how DL is used in phase image processing. Finally, we summarize the work in DL for PR and outlook on how to better use DL to improve the reliability and efficiency in PR. Furthermore, we present a live-updating resource (https://github.com/kqwang/phase-recovery) for readers to learn more about PR.