Electron holography is a useful tool for analyzing functional properties, such as electromagnetic fields and strains of materials and devices. The performance of electron holography is limited by the “shot noise” inherent in electron micrographs (holograms), which are composed of a finite number of electrons. A promising approach for addressing this issue is to use mathematical and machine learning-based image-processing techniques for hologram denoising. With the advancement of information science, denoising methods have become capable of extracting signals that are completely buried in noise, and they are being applied to electron microscopy, including electron holography. However, these advanced denoising methods are complex and have many parameters to be tuned; therefore, it is necessary to understand their principles in depth and use them carefully. Herein, we present an overview of the principles and usage of sparse coding, wavelet hidden Markov model, and tensor decomposition, which have been applied to electron holography. We also present evaluation results for the denoising performance of these methods obtained through their application to simulated and experimentally recorded holograms. Our analysis, review, and comparison of the methods clarify the impact of denoising on electron-holography research.

中文翻译：

---

利用基于数学和机器学习的去噪技术增强电子全息术的性能

电子全息术是分析功能特性的有用工具，例如电磁场以及材料和设备的应变。电子全息术的性能受到电子显微照片（全息图）固有的“散粒噪声”的限制，电子显微照片由有限数量的电子组成。解决这个问题的一个有前途的方法是使用基于数学和机器学习的图像处理技术进行全息图去噪。随着信息科学的进步，去噪方法已经能够提取完全淹没在噪声中的信号，并且它们正在应用于电子显微镜，包括电子全息术。然而，这些先进的去噪方法比较复杂，需要调整的参数很多；因此，有必要深入理解它们的原理并谨慎使用它们。在此，我们概述了应用于电子全息术的稀疏编码、小波隐马尔可夫模型和张量分解的原理和用法。我们还提出了通过将这些方法应用于模拟和实验记录的全息图而获得的去噪性能的评估结果。我们对这些方法的分析、回顾和比较阐明了去噪对电子全息研究的影响。