# Coordinate-based Neural Network for Fourier Phase Retrieval

arXiv: https://arxiv.org/abs/2311.14925 · HTML: https://mlsanity.com/paper/2311.14925/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 33 references that are in the map.
- First posted on arXiv 25 Nov 2023.

## Builds on (most cited first, 16 of 16)

- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Deep Local Shapes: Learning Local SDF Priors for Detailed 3D Reconstruction](https://mlsanity.com/paper/2003.10983/) (2020)
- [Neural Unsigned Distance Fields for Implicit Function Learning](https://mlsanity.com/paper/2010.13938/) (2020)
- [WIRE: Wavelet Implicit Neural Representations](https://mlsanity.com/paper/2301.05187/) (2023)
- [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)
- [DINER: Disorder-Invariant Implicit Neural Representation](https://mlsanity.com/paper/2211.07871/) (2022)
- [AutoPhaseNN: Unsupervised Physics-aware Deep Learning of 3D Nanoscale Bragg Coherent Diffraction Imaging](https://mlsanity.com/paper/2109.14053/) (2021)
- [Real-time coherent diffraction inversion using deep generative networks](https://mlsanity.com/paper/1806.03992/) (2018)
- [Three-dimensional Coherent X-ray Diffraction Imaging via Deep Convolutional Neural Networks](https://mlsanity.com/paper/2103.00001/) (2021)
- [Practical Phase Retrieval Using Double Deep Image Priors](https://mlsanity.com/paper/2211.00799/) (2022)
- [Adaptive 3D convolutional neural network-based reconstruction method for 3D coherent diffraction imaging](https://mlsanity.com/paper/2008.10094/) (2020)
- [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)
- [FPM-INR: Fourier ptychographic microscopy image stack reconstruction using implicit neural representations](https://mlsanity.com/paper/2310.18529/) (2023)

## Abstract (arXiv)

Fourier phase retrieval is essential for high-definition imaging of nanoscale structures across diverse fields, notably coherent diffraction imaging. This study presents the Single impliCit neurAl Network (SCAN), a tool built upon coordinate neural networks meticulously designed for enhanced phase retrieval performance. Remedying the drawbacks of conventional iterative methods which are easiliy trapped into local minimum solutions and sensitive to noise, SCAN adeptly connects object coordinates to their amplitude and phase within a unified network in an unsupervised manner. While many existing methods primarily use Fourier magnitude in their loss function, our approach incorporates both the predicted magnitude and phase, enhancing retrieval accuracy. Comprehensive tests validate SCAN's superiority over traditional and other deep learning models regarding accuracy and noise robustness. We also demonstrate that SCAN excels in the ptychography setting.