# Non-Iterative Phase Retrieval With Cascaded Neural Networks

arXiv: https://arxiv.org/abs/2106.10195 · HTML: https://mlsanity.com/paper/2106.10195/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 26 references that are in the map.
- First posted on arXiv 18 Jun 2021.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Context Encoders: Feature Learning by Inpainting](https://mlsanity.com/paper/1604.07379/) (2016)
- [Deep Learning for Classical Japanese Literature](https://mlsanity.com/paper/1812.01718/) (2018)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [A Deep Cascade of Convolutional Neural Networks for Dynamic MR Image Reconstruction](https://mlsanity.com/paper/1704.02422/) (2017)
- [Phase Retrieval Under a Generative Prior](https://mlsanity.com/paper/1807.04261/) (2018)
- [prDeep: Robust Phase Retrieval with a Flexible Deep Network](https://mlsanity.com/paper/1803.00212/) (2018)
- [Deep Iterative Reconstruction for Phase Retrieval](https://mlsanity.com/paper/1904.11301/) (2019)
- [Online Regularization by Denoising with Applications to Phase Retrieval](https://mlsanity.com/paper/1909.02040/) (2019)
- [Phase Retrieval Using Conditional Generative Adversarial Networks](https://mlsanity.com/paper/1912.04981/) (2019)

## Built on by (most cited first, 6 of 6)

- [On the use of deep learning for phase recovery](https://mlsanity.com/paper/2308.00942/) (2023)
- [SiSPRNet: End-to-End Learning for Single-Shot Phase Retrieval](https://mlsanity.com/paper/2205.11434/) (2022)
- [PR-DAD: Phase Retrieval Using Deep Auto-Decoders](https://mlsanity.com/paper/2204.09051/) (2022)
- [Optimizing Intermediate Representations of Generative Models for Phase Retrieval](https://mlsanity.com/paper/2205.15617/) (2022)
- [Towards Practical Single-shot Phase Retrieval with Physics-Driven Deep Neural Network](https://mlsanity.com/paper/2208.08604/) (2022)
- [Res-U2Net: Untrained Deep Learning for Phase Retrieval and Image Reconstruction](https://mlsanity.com/paper/2404.06657/) (2024)

## Abstract (arXiv)

Fourier phase retrieval is the problem of reconstructing a signal given only the magnitude of its Fourier transformation. Optimization-based approaches, like the well-established Gerchberg-Saxton or the hybrid input output algorithm, struggle at reconstructing images from magnitudes that are not oversampled. This motivates the application of learned methods, which allow reconstruction from non-oversampled magnitude measurements after a learning phase. In this paper, we want to push the limits of these learned methods by means of a deep neural network cascade that reconstructs the image successively on different resolutions from its non-oversampled Fourier magnitude. We evaluate our method on four different datasets (MNIST, EMNIST, Fashion-MNIST, and KMNIST) and demonstrate that it yields improved performance over other non-iterative methods and optimization-based methods.