Electron tomography is widely employed for the 3D morphological characterization at the nanoscale. In recent years, there has been a growing interest in analytical electron tomography (AET) as it is capable of providing 3D information about the elemental composition, chemical bonding and optical/electronic properties of nanomaterials. AET requires advanced reconstruction algorithms as the datasets often consist of a very limited number of projections. Total variation (TV)-based compressed sensing approaches were shown to provide high-quality reconstructions from undersampled datasets, but staircasing artefacts can appear when the assumption about piecewise constancy does not hold. In this paper, we compare higher-order TV and wavelet-based approaches for AET applications and provide an open-source Python toolbox, Pyetomo, containing 2D and 3D implementations of both methods. A highly sampled STEM-HAADF dataset of an Er-doped porous Si sample and a heavily undersampled STEM-EELS dataset of a Ge-rich GeSbTe (GST) thin film annealed at 450°C are used to evaluate the performance of the different approaches. We show that polynomial annihilation with order 3 (HOTV₃) and the Bior4.4 wavelet outperform the classical TV minimization and the related Haar wavelet.

电子断层扫描被广泛用于纳米尺度的3D形态表征。近年来，对分析电子断层扫描（AET）的兴趣日益浓厚，因为它能够提供有关纳米材料的元素组成，化学键合和光学/电子性质的3D信息。由于数据集通常由数量非常有限的投影组成，因此AET需要先进的重建算法。已显示基于总变异（TV）的压缩传感方法可从欠采样数据集中提供高质量的重建，但是当关于分段恒定性的假设不成立时，可能会出现楼梯伪影。在本文中，我们比较了针对AET应用程序的高阶电视和基于小波的方法，并提供了一个开源Python工具箱Pyetomo，其中包含这两种方法的2D和3D实现。掺Er多孔硅样品的高采样STEM-HAADF数据集和450°C退火的富含Ge的GeSbTe（GST）薄膜的STEM-EELS数据集严重欠采样，用于评估不同方法的性能。我们表明，多项式an灭与阶数3（HOTV ₃）和Bior4.4小波的性能优于经典的电视最小化和相关的Haar小波。