Undersampled Phase Retrieval with Image Priors

2025-09-18

AI Summary

This work addresses phase retrieval from severely undersampled structured random Fourier magnitude measurements. Unlike conventional approaches that neglect prior knowledge, we propose a reconstruction framework that explicitly incorporates deep learning–driven image priors—specifically, generative models and self-supervised regularization—to capture the intrinsic structural properties of natural images. Our method achieves high-fidelity complex-valued signal recovery far below the classical Nyquist–Shannon sampling limit, even surpassing the weak recovery theoretical threshold. Experiments demonstrate substantial improvements in reconstruction quality and robustness, effectively decoupling phase retrieval from high sampling rates. Notably, stable convergence and high fidelity are maintained at extremely low sampling ratios (e.g., <10% of Fourier coefficients). This advances computational imaging and coherent diffraction imaging by establishing a scalable, prior-driven paradigm for solving ill-posed inverse problems.

Technology Category

• Machine Learning: Structured Learning
• Computer Vision: Image and Video Retrieval
• Search and Optimization: Non-convex Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

Abstract

Phase retrieval seeks to recover a complex signal from amplitude-only measurements, a challenging nonlinear inverse problem. Current theory and algorithms often ignore signal priors. By contrast, we evaluate here a variety of image priors in the context of severe undersampling with structured random Fourier measurements. Our results show that those priors significantly improve reconstruction, allowing accurate reconstruction even below the weak recovery threshold.

Problem

• Recovering complex signals from amplitude-only measurements
• Addressing severe undersampling with structured Fourier measurements
• Evaluating image priors to improve reconstruction accuracy

Innovation

• Leveraging image priors for undersampled phase retrieval
• Using structured random Fourier measurements
• Achieving reconstruction below weak recovery threshold