Maximum-likelihood estimation in ptychography in the presence of Poisson-Gaussian noise statistics

TL;DR

This paper introduces a maximum-likelihood based method for ptychography that explicitly models mixed Poisson-Gaussian noise, significantly improving image reconstruction quality under low SNR conditions.

Contribution

It presents a novel loss function and optimization approach that incorporate mixed noise statistics, addressing limitations of previous methods assuming only Poisson noise.

Findings

Outperforms conventional methods in noisy conditions

Enhances image quality in experimental and numerical tests

Provides a practical adjustment for noise modeling in ptychography

Abstract

Optical measurements often exhibit mixed Poisson-Gaussian noise statistics, which hampers image quality, particularly under low signal-to-noise ratio (SNR) conditions. Computational imaging falls short in such situations when solely Poissonian noise statistics are assumed. In response to this challenge, we define a loss function that explicitly incorporates this mixed noise nature. By using maximum-likelihood estimation, we devise a practical method to account for camera readout noise in gradient-based ptychography optimization. Our results, based on both experimental and numerical data, demonstrate that this approach outperforms the conventional one, enabling enhanced image reconstruction quality under challenging noise conditions through a straightforward methodological adjustment.