# Towards Practical Single-shot Phase Retrieval with Physics-Driven Deep Neural Network

arXiv: https://arxiv.org/abs/2208.08604 · HTML: https://mlsanity.com/paper/2208.08604/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 43 references that are in the map.
- First posted on arXiv 18 Aug 2022.

## Builds on (most cited first, 22 of 22)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Phase Retrieval via Wirtinger Flow: Theory and Algorithms](https://mlsanity.com/paper/1407.1065/) (2014)
- [Solving Random Quadratic Systems of Equations Is Nearly as Easy as Solving Linear Systems](https://mlsanity.com/paper/1505.05114/) (2015)
- [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)
- [Phase Retrieval from Coded Diffraction Patterns](https://mlsanity.com/paper/1310.3240/) (2013)
- [Learning to Synthesize: Robust Phase Retrieval at Low Photon counts](https://mlsanity.com/paper/1907.11713/) (2019)
- [PhaseGAN: A deep-learning phase-retrieval approach for unpaired datasets](https://mlsanity.com/paper/2011.08660/) (2020)
- [Deep Iterative Reconstruction for Phase Retrieval](https://mlsanity.com/paper/1904.11301/) (2019)
- [Phase Retrieval Using Conditional Generative Adversarial Networks](https://mlsanity.com/paper/1912.04981/) (2019)
- [Three-dimensional Coherent X-ray Diffraction Imaging via Deep Convolutional Neural Networks](https://mlsanity.com/paper/2103.00001/) (2021)
- [DeepPhaseCut: Deep Relaxation in Phase for Unsupervised Fourier Phase Retrieval](https://mlsanity.com/paper/2011.10475/) (2020)
- [SiSPRNet: End-to-End Learning for Single-Shot Phase Retrieval](https://mlsanity.com/paper/2205.11434/) (2022)
- [Non-Iterative Phase Retrieval With Cascaded Neural Networks](https://mlsanity.com/paper/2106.10195/) (2021)
- [Phase Retrieval using Expectation Consistent Signal Recovery Algorithm based on Hypernetwork](https://mlsanity.com/paper/2101.04348/) (2021)
- [Robust Phase Retrieval with Green Noise Binary Masks](https://mlsanity.com/paper/2012.09410/) (2020)

## Abstract (arXiv)

Phase retrieval (PR), a long-established challenge for recovering a complex-valued signal from its Fourier intensity-only measurements, has attracted considerable attention due to its widespread applications in digital imaging. Recently, deep learning-based approaches were developed that achieved some success in single-shot PR. These approaches require a single Fourier intensity measurement without the need to impose any additional constraints on the measured data. Nevertheless, vanilla deep neural networks (DNN) do not give good performance due to the substantial disparity between the input and output domains of the PR problems. Physics-informed approaches try to incorporate the Fourier intensity measurements into an iterative approach to increase the reconstruction accuracy. It, however, requires a lengthy computation process, and the accuracy still cannot be guaranteed. Besides, many of these approaches work on simulation data that ignore some common problems such as saturation and quantization errors in practical optical PR systems. In this paper, a novel physics-driven multi-scale DNN structure dubbed PPRNet is proposed. Similar to other deep learning-based PR methods, PPRNet requires only a single Fourier intensity measurement. It is physics-driven that the network is guided to follow the Fourier intensity measurement at different scales to enhance the reconstruction accuracy. PPRNet has a feedforward structure and can be end-to-end trained. Thus, it is much faster and more accurate than the traditional physics-driven PR approaches. Extensive simulations and experiments on a practical optical platform were conducted. The results demonstrate the superiority and practicality of the proposed PPRNet over the traditional learning-based PR methods.