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Coordinate-based Neural Network for Fourier Phase Retrieval

Tingyou Li, Zixin Xu, Yong S. Chu, Xiaojing Huang, Jizhou Li

TL;DR

The paper tackles Fourier phase retrieval by introducing SCAN, a single coordinate-based neural network that jointly predicts object amplitude and phase in an unsupervised framework. It leverages an implicit representation with a sinusoidal-activated MLP and a novel loss combining Fourier magnitude and distilled Fourier phase terms to guide training. SCAN demonstrates superior accuracy, noise robustness, and stability compared with traditional iterative methods and several deep-learning baselines, in both coherent diffraction imaging and ptychography, and offers faster performance with reduced hyperparameter burden. The work suggests promising extensions to 3D Bragg Ptychography and broader phase-retrieval problems in nanoscale imaging.

Abstract

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.

Coordinate-based Neural Network for Fourier Phase Retrieval

TL;DR

The paper tackles Fourier phase retrieval by introducing SCAN, a single coordinate-based neural network that jointly predicts object amplitude and phase in an unsupervised framework. It leverages an implicit representation with a sinusoidal-activated MLP and a novel loss combining Fourier magnitude and distilled Fourier phase terms to guide training. SCAN demonstrates superior accuracy, noise robustness, and stability compared with traditional iterative methods and several deep-learning baselines, in both coherent diffraction imaging and ptychography, and offers faster performance with reduced hyperparameter burden. The work suggests promising extensions to 3D Bragg Ptychography and broader phase-retrieval problems in nanoscale imaging.

Abstract

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.
Paper Structure (12 sections, 8 equations, 4 figures, 6 tables)

This paper contains 12 sections, 8 equations, 4 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Methods
  3. Image Coordination
  4. Backbone of Main Network
  5. Loss Function
  6. Experiments
  7. Experimental setup
  8. Model Training
  9. Results
  10. Results of CDI setting
  11. Results of Ptychography setting
  12. Conclusions

Figures (4)

  • Figure 1: Illustration of the proposed SCAN approach for Fourier phase retrieval.
  • Figure 2: Best performance of different methods under noise-free condition
  • Figure 3: (a) Ablation study of different loss functions under different noise levels ($\sigma=0, 10, 100$, and 1000); (b) comparison of noise robustness across different methods; (c) ablation study of network architectures.
  • Figure 4: Ptychographic reconstruction comparisons between ePIE and SCAN at overlap rates of 30%, 50%, and 70%.