Spectral method for low-dose Poisson and Bernoulli phase retrieval
Sjoerd Dirksen, Felix Krahmer, Patricia Römer, Palina Salanevich
TL;DR
This work analyzes a spectral method for phaseless reconstruction under Poisson and Bernoulli noise in a low-dose imaging regime with Gaussian measurements. By formulating a constrained spectral objective and analyzing the random matrix $Y = \frac{1}{m}\sum_i y_i a_i a_i^T$, the authors derive explicit $\mathbb{E}[Y]$ expressions for both noise models and establish high-probability bounds that link the top eigenvector to the ground-truth signal $x$. They prove recovery guarantees with near-optimal sampling complexity, showing how the required number of measurements grows only logarithmically with the dose parameter $\alpha$. The results quantify the dose-sampling trade-off and provide theoretical support for using spectral phase retrieval in ultra-low-dose biological imaging contexts.
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.