# Noise reduction of low-dose electron holograms using the wavelet hidden Markov model

## TL;DR

This paper shows that using a wavelet hidden Markov model can reduce noise in electron holograms, allowing for lower electron doses while maintaining precision in measuring electric fields.

## Contribution

The study demonstrates that wavelet hidden Markov model denoising improves low-dose electron holography precision for weak electric fields.

## Key findings

- WHMM denoising reduces electron dose by half without sacrificing charge determination precision.
- WHMM enables clear visualization of weak electric fields at low electron doses.
- The method is beneficial for studying electron-beam-sensitive materials.

## Abstract

The precision in electron holography studies on electrostatic and magnetic fields depends on the image quality of an electron hologram. Enhancing the image quality of electron holograms is essential for the comprehensive analysis of weak electromagnetic fields; however, extended electron beam irradiation can lead to undesirable radiation damage and contamination. Recent studies have demonstrated that noise reduction using the wavelet hidden Markov model (WHMM) can improve the precision of phase analysis for limited thin-foiled crystals. In this study, we examine the effects of WHMM-based denoising on the electron holography data of weakly charged nanoparticles collected under low-electron-dose conditions. The results indicate that effective noise reduction with the WHMM allows for a reduction in the magnitude of the electron dose by approximately half relative to data collection without WHMM denoising, while maintaining the same level of charge determination precision: less than one elementary charge. Notably, at a low electron dose of 0.40 e−/pixel, WHMM denoising enables the clear visualization of a weak stray electric field outside a charged latex sphere. This method offers significant advantages for electron holography studies of electron-beam-sensitive materials requiring minimal time for electron exposure.