# Optimizing Intermediate Representations of Generative Models for Phase Retrieval

arXiv: https://arxiv.org/abs/2205.15617 · HTML: https://mlsanity.com/paper/2205.15617/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 44 references that are in the map.
- First posted on arXiv 31 May 2022.

## Builds on (most cited first, 27 of 27)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [In-Domain GAN Inversion for Real Image Editing](https://mlsanity.com/paper/2004.00049/) (2020)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [Semantic Image Inpainting with Deep Generative Models](https://mlsanity.com/paper/1607.07539/) (2016)
- [Adding Gradient Noise Improves Learning for Very Deep Networks](https://mlsanity.com/paper/1511.06807/) (2015)
- [Phase Retrieval via Wirtinger Flow: Theory and Algorithms](https://mlsanity.com/paper/1407.1065/) (2014)
- [Invertible generative models for inverse problems: mitigating representation error and dataset bias](https://mlsanity.com/paper/1905.11672/) (2019)
- [Phase Retrieval Under a Generative Prior](https://mlsanity.com/paper/1807.04261/) (2018)
- [Intermediate Layer Optimization for Inverse Problems using Deep Generative Models](https://mlsanity.com/paper/2102.07364/) (2021)
- [prDeep: Robust Phase Retrieval with a Flexible Deep Network](https://mlsanity.com/paper/1803.00212/) (2018)
- [Solving Systems of Random Quadratic Equations via Truncated Amplitude Flow](https://mlsanity.com/paper/1605.08285/) (2016)
- [Alternating Phase Projected Gradient Descent with Generative Priors for Solving Compressive Phase Retrieval](https://mlsanity.com/paper/1903.02707/) (2019)
- [Towards Sample-Optimal Compressive Phase Retrieval with Sparse and Generative Priors](https://mlsanity.com/paper/2106.15358/) (2021)
- [Phase Retrieval Using Conditional Generative Adversarial Networks](https://mlsanity.com/paper/1912.04981/) (2019)
- [Solving Phase Retrieval with a Learned Reference](https://mlsanity.com/paper/2007.14621/) (2020)
- [When deep denoising meets iterative phase retrieval](https://mlsanity.com/paper/2003.01792/) (2020)
- [Phase Retrieval with Holography and Untrained Priors: Tackling the Challenges of Low-Photon Nanoscale Imaging](https://mlsanity.com/paper/2012.07386/) (2020)
- [Non-Iterative Phase Retrieval With Cascaded Neural Networks](https://mlsanity.com/paper/2106.10195/) (2021)
- [Generator Surgery for Compressed Sensing](https://mlsanity.com/paper/2102.11163/) (2021)
- [A Closer Look at Reference Learning for Fourier Phase Retrieval](https://mlsanity.com/paper/2110.13688/) (2021)

## Built on by (most cited first, 1 of 1)

- [On the use of deep learning for phase recovery](https://mlsanity.com/paper/2308.00942/) (2023)

## Abstract (arXiv)

Phase retrieval is the problem of reconstructing images from magnitude-only measurements. In many real-world applications the problem is underdetermined. When training data is available, generative models allow optimization in a lower-dimensional latent space, hereby constraining the solution set to those images that can be synthesized by the generative model. However, not all possible solutions are within the range of the generator. Instead, they are represented with some error. To reduce this representation error in the context of phase retrieval, we first leverage a novel variation of intermediate layer optimization (ILO) to extend the range of the generator while still producing images consistent with the training data. Second, we introduce new initialization schemes that further improve the quality of the reconstruction. With extensive experiments on the Fourier phase retrieval problem and thorough ablation studies, we can show the benefits of our modified ILO and the new initialization schemes. Additionally, we analyze the performance of our approach on the Gaussian phase retrieval problem.