Spectral method for low-dose Poisson and Bernoulli phase retrieval

TL;DR

This paper analyzes a spectral method for phase retrieval under low-dose Poisson and Bernoulli noise, providing theoretical guarantees and insights into the dose-sampling trade-off in biological imaging.

Contribution

It introduces recovery guarantees for spectral methods in Poisson and Bernoulli noise models, specifically in low-dose biological imaging scenarios.

Findings

Provides quantitative bounds on reconstruction accuracy.

Characterizes the dose-sampling complexity trade-off.

Extends spectral methods to Poisson and Bernoulli noise models.

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.