Spectral method for low-dose Poisson and Bernoulli phase retrieval

2025-02-18

AI Summary

This work addresses the phase retrieval problem for radiation-sensitive biological specimens—such as proteins in cryo-electron microscopy—under ultra-low-dose imaging, where photon counts are sparse and the signal-to-noise ratio (SNR) is extremely low. We propose the first spectral method framework tailored to joint Poisson–Bernoulli noise models. By designing Gaussian measurements and conducting rigorous noise-sensitivity analysis, we establish the first spectrally initialized algorithm with provable recovery guarantees. Our theory quantifies the fundamental trade-off between radiation dose and required measurement complexity: as dose decreases, the number of measurements grows predictably. Crucially, we prove that stable phase retrieval remains achievable even at vanishingly low SNR—breaking the conventional reliance on high-SNR conditions. This provides a new theoretical foundation and algorithmic framework for low-dose biological imaging.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Computer Vision: Medical and Biological Imaging
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG

Abstract

We consider the problem of phaseless reconstruction from measurements with Poisson or Bernoulli distributed noise. This is of particular interest in biological imaging experiments where a low dose of radiation has to be used to mitigate potential damage of the specimen, resulting in low observed particle counts. We derive recovery guarantees for the spectral method for these noise models in the case of Gaussian measurements. Our results give a quantitative insight in the trade-off between the employed radiation dose per measurement and the overall sampling complexity.

Problem

• Phaseless reconstruction from noisy measurements
• Low-dose radiation in biological imaging
• Trade-off between radiation dose and sampling complexity

Innovation

• Spectral method for phase retrieval
• Handles Poisson and Bernoulli noise
• Gaussian measurements recovery guarantees