We try to improve the limit of the phase estimation of the interference fringe at low electron dose levels in electron holography by a noise reduction method. In this paper, we focus on unsupervised approaches to apply it to electron beam-sensitive and unknown samples and describe an overview of denoising methods used widely in image processing, such as wiener filter, total variation denoising, nonlocal mean filters and wavelet thresholding. We compare the wavelet hidden Markov model (WHMM) denoising that we have studied so far with the other conventional noise reduction methods. We evaluate the denoise performance of each method using the peak signal-to-noise ratio between noise-free and the target holograms (noisy or denoised holograms) and the root mean-square error (RMSE) between the true phase of the fringe and the measured phase by the discrete Fourier transform phase estimator. We show the denoised holograms for simulation and experimental data by using each noise reduction method and then discuss evaluation indexes obtained from these denoised holograms. From experimental results, it can be seen that the WHMM denoising can reduce the RMSE of fringe phase to about 1/4.5 for noisy simulation holograms and it has stable and good performance for noise reduction of observed holograms with various image qualities.

中文翻译：

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使用降噪方法提高电子全息相位估计的精度

我们尝试通过降噪方法提高电子全息术中低电子剂量水平下干涉条纹的相位估计极限。在本文中，我们专注于将其应用于电子束敏感和未知样本的无监督方法，并概述广泛用于图像处理的去噪方法，例如维纳滤波器、全变差去噪、非局部均值滤波器和小波阈值。我们将迄今为止研究的小波隐马尔可夫模型 (WHMM) 降噪与其他传统降噪方法进行了比较。我们使用无噪声和目标全息图（有噪声或去噪全息图）之间的峰值信噪比以及条纹真实相位与目标全息图之间的均方根误差 (RMSE) 来评估每种方法的去噪性能。由离散傅立叶变换相位估计器测量的相位。我们通过使用每种降噪方法显示用于模拟和实验数据的去噪全息图，然后讨论从这些去噪全息图中获得的评估指标。从实验结果可以看出，WHMM去噪可以将噪声模拟全息图的条纹相位均方根误差降低到1/4.5左右，并且对于观察到的各种图像质量的全息图的降噪性能稳定良好。我们通过使用每种降噪方法显示用于模拟和实验数据的去噪全息图，然后讨论从这些去噪全息图中获得的评估指标。从实验结果可以看出，WHMM去噪可以将噪声模拟全息图的条纹相位均方根误差降低到1/4.5左右，并且对于观察到的各种图像质量的全息图的降噪性能稳定良好。我们通过使用每种降噪方法显示用于模拟和实验数据的去噪全息图，然后讨论从这些去噪全息图中获得的评估指标。从实验结果可以看出，WHMM去噪可以将噪声模拟全息图的条纹相位均方根误差降低到1/4.5左右，并且对于观察到的各种图像质量的全息图的降噪性能稳定良好。