# Untrained neural network embedded Fourier phase retrieval from few measurements

arXiv: https://arxiv.org/abs/2307.08717 · HTML: https://mlsanity.com/paper/2307.08717/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 52 references that are in the map.
- First posted on arXiv 16 Jul 2023.

## Builds on (most cited first, 23 of 23)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Deep Decoder: Concise Image Representations from Untrained Non-convolutional Networks](https://mlsanity.com/paper/1810.03982/) (2018)
- [Global Convergence of ADMM in Nonconvex Nonsmooth Optimization](https://mlsanity.com/paper/1511.06324/) (2015)
- [Phase Retrieval Under a Generative Prior](https://mlsanity.com/paper/1807.04261/) (2018)
- [Convergence Analysis of Alternating Direction Method of Multipliers for a Family of Nonconvex Problems](https://mlsanity.com/paper/1410.1390/) (2014)
- [Regularization by Denoising via Fixed-Point Projection (RED-PRO)](https://mlsanity.com/paper/2008.00226/) (2020)
- [prDeep: Robust Phase Retrieval with a Flexible Deep Network](https://mlsanity.com/paper/1803.00212/) (2018)
- [Denoising and Regularization via Exploiting the Structural Bias of Convolutional Generators](https://mlsanity.com/paper/1910.14634/) (2019)
- [Compressive sensing with un-trained neural networks: Gradient descent finds the smoothest approximation](https://mlsanity.com/paper/2005.03991/) (2020)
- [Algorithmic Guarantees for Inverse Imaging with Untrained Network Priors](https://mlsanity.com/paper/1906.08763/) (2019)
- [Deep Phase Decoder: Self-calibrating phase microscopy with an untrained deep neural network](https://mlsanity.com/paper/2001.09803/) (2020)
- [Alternating Phase Projected Gradient Descent with Generative Priors for Solving Compressive Phase Retrieval](https://mlsanity.com/paper/1903.02707/) (2019)
- [Fast L1-L2 minimization via a proximal operator](https://mlsanity.com/paper/1609.09530/) (2016)
- [Diffraction tomography with a deep image prior](https://mlsanity.com/paper/1912.05330/) (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)
- [Blind Ptychographic Phase Retrieval via Convergent Alternating Direction Method of Multipliers](https://mlsanity.com/paper/1808.05802/) (2018)
- [Phase retrieval for Bragg coherent diffraction imaging at high X-ray energies](https://mlsanity.com/paper/1811.06181/) (2018)
- [Solving Phase Retrieval via Graph Projection Splitting](https://mlsanity.com/paper/1910.08714/) (2019)

## Abstract (arXiv)

Fourier phase retrieval (FPR) is a challenging task widely used in various applications. It involves recovering an unknown signal from its Fourier phaseless measurements. FPR with few measurements is important for reducing time and hardware costs, but it suffers from serious ill-posedness. Recently, untrained neural networks have offered new approaches by introducing learned priors to alleviate the ill-posedness without requiring any external data. However, they may not be ideal for reconstructing fine details in images and can be computationally expensive. This paper proposes an untrained neural network (NN) embedded algorithm based on the alternating direction method of multipliers (ADMM) framework to solve FPR with few measurements. Specifically, we use a generative network to represent the image to be recovered, which confines the image to the space defined by the network structure. To improve the ability to represent high-frequency information, total variation (TV) regularization is imposed to facilitate the recovery of local structures in the image. Furthermore, to reduce the computational cost mainly caused by the parameter updates of the untrained NN, we develop an accelerated algorithm that adaptively trades off between explicit and implicit regularization. Experimental results indicate that the proposed algorithm outperforms existing untrained NN-based algorithms with fewer computational resources and even performs competitively against trained NN-based algorithms.