A Gaussian Parameterization for Direct Atomic Structure Identification in Electron Tomography

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.

Missing Wedge Inpainting and Joint Alignment in Electron Tomography through Implicit Neural Representations

Electron tomography is a powerful tool for understanding the morphology of materials in three dimensions, but conventional reconstruction algorithms typically suffer from missing-wedge artifacts and data misalignment imposed by experimental constraints. Recently proposed supervised machine-learning-enabled reconstruction methods to address these challenges rely on training data and are therefore difficult to generalize across materials systems. We propose a fully self-supervised implicit neural representation (INR) approach using a neural network as a regularizer. Our approach enables fast inline alignment through pose optimization, missing wedge inpainting, and denoising of low dose datasets via model regularization using only a single dataset. We apply our method to simulated and experimental data and show that it produces high-quality tomograms from diverse and information limited datasets. Our results show that INR-based self-supervised reconstructions offer high fidelity reconstructions with minimal user input and preprocessing, and can be readily applied to a wide variety of materials samples and experimental parameters.

Deep generative priors for robust and efficient electron ptychography

Electron ptychography enables dose-efficient atomic-resolution imaging, but conventional reconstruction algorithms suffer from noise sensitivity, slow convergence, and extensive manual hyperparameter tuning for regularization, especially in three-dimensional multislice reconstructions. We introduce a deep generative prior (DGP) framework for electron ptychography that uses the implicit regularization of convolutional neural networks to address these challenges. Two DGPs parameterize the complex-valued sample and probe within an automatic-differentiation mixed-state multislice forward model. Compared to pixel-based reconstructions, DGPs offer four key advantages: (i) greater noise robustness and improved information limits at low dose; (ii) markedly faster convergence, especially at low spatial frequencies; (iii) improved depth regularization; and (iv) minimal user-specified regularization. The DGP framework promotes spatial coherence and suppresses high-frequency noise without extensive tuning, and a pre-training strategy stabilizes reconstructions. Our results establish DGP-enabled ptychography as a robust approach that reduces expertise barriers and computational cost, delivering robust, high-resolution imaging across diverse materials and biological systems.