A Gaussian Parameterization for Direct Atomic Structure Identification in Electron Tomography

TL;DR

This work reframes atomic electron tomography as direct optimization over atomic parameters by representing each atom as a Gaussian with learnable position, size, and amplitude. By introducing isotropy and interatomic-distance priors and allowing the model to adapt the number of Gaussians, the method yields a 1-to-1 Gaussian-to-atom mapping and improved robustness to missing-wedge and imaging artifacts. Evaluations on simulated nanoparticles and preliminary experimental data show competitive reconstruction quality with full data and superior atom identification under limited-angle conditions, outperforming traditional voxel-based pipelines. The approach promises streamlined, physically plausible atomic structure identification and could accelerate materials characterization in TEM studies. Overall, it demonstrates that a Gaussian-parameterized, priors-guided framework can directly uncover atomic architectures from projection data with reduced manual intervention.

Abstract

Atomic electron tomography (AET) enables the determination of 3D atomic structures by acquiring a sequence of 2D tomographic projection measurements of a particle and then computationally solving for its underlying 3D representation. Classical tomography algorithms solve for an intermediate volumetric representation that is post-processed into the atomic structure of interest. In this paper, we reformulate the tomographic inverse problem to solve directly for the locations and properties of individual atoms. We parameterize an atomic structure as a collection of Gaussians, whose positions and properties are learnable. This representation imparts a strong physical prior on the learned structure, which we show yields improved robustness to real-world imaging artifacts. Simulated experiments and a proof-of-concept result on experimentally-acquired data confirm our method's potential for practical applications in materials characterization and analysis with Transmission Electron Microscopy (TEM). Our code is available at https://github.com/nalinimsingh/gaussian-atoms.

Figures (10)

• Figure 1: Traditional methods for atomic electron tomography (AET) first computationally reconstruct a volumetric image of the sample and then identify the underlying atomic structure via a combination of algorithmic peak finding and manual post-processing. Our proposed method simplifies this workflow to solve for the 3D properties of each atom directly.
• Figure 2: Tomographic acquisition setup showing the sample that will be reconstructed (dark blue) tilted at various angles (dotted purple). Several particles outside of the region of interest (light blue) lie on the sample holder, and at high tilt angles (right), interfere with the acquired projection measurements. This results in the missing wedge problem where projection measurements cannot be acquired at certain angles, yielding an underdetermined inverse problem. Even beyond the missing wedge, angles maybe sampled sparsely for dose reduction.
• Figure 3: A single (central) slice of the 3D reconstruction and its corresponding atom identification for the simulated gold nanoparticle, for both the full-data case where all projection angles are available and the case of limited data (angles between -70° and -68° in 3° increments). We compare our reconstruction, which directly solves for atom properties, to several baseline algorithms that use volumetric reconstruction followed by atom tracing: Filtered Backprojection (FBP), Simultaneous Algebraic Reconstruction Technique (SART), and Implicit Neural Representation (INR). All methods perform fairly well in the case with no missing wedge, but the baseline performance degrades in the missing wedge case. Our method accurately finds the majority of atoms without yielding excessive false positives.
• Figure 4: Quantitative results on the particles in our dataset. All methods achieve a fairly high true positive rate on data with all angles, and this performance degrades slightly in the limited angle setting. However, other methods' performance degrades dramatically in terms of false positive rate in the limited data setting, while our method is less affected. Similarly, the reconstruction quality of other methods decreases more dramatically in the limited data setting.
• Figure 5: Ablation study showing the effect of physical constraints on our method's structure identification. Top row: atom localization for an idealized slice of the simulated double-wall Zirconium-Tellurium carbon nanotube with all projection angles and no noise or probe blur. Bottom row: learned Gaussian amplitude for matched atoms. When the isotropic and minimum distance constraints are not included, multiple Gaussians are fit to each atom, yielding an inaccurate structural representation. Each Gaussian is typically fit with a lower amplitude to compensate for the presence of several other atoms close by (note the different x-axis scales). Our physical constraints force a 1-to-1 correspondence between Gaussians and atoms, which in turn allows their learned opacities to distribute separably by atomic species.