The advancement of scanning transmission electron microscopy (STEM) with spherical aberration correctors has enabled atomic-scale imaging with resolutions reaching 1 Å. This allows for quantitative analysis of atomic positions to study structure-property relationships, which often involve picometer-scale shifts in atomic positions. However, challenges remain in reliably characterizing these transitions due to limited spatial resolution and noise in STEM images. Current methods often rely on multiple image summation for signal-to-noise ratio (SNR) enhancement, but this increases electron dose and can damage the sample. Single-image enhancement techniques, such as Wiener filtering and band-pass filtering, or advanced methods like principal component analysis (PCA), non-local means filtering, and BM3D filtering, have been applied but are often less effective for the dominant Poisson noise in STEM images. Model-based estimation methods, using 2D Gaussian or quadratic functions, have been employed to improve accuracy but can be computationally expensive. The center of mass method is a simpler alternative, but its accuracy depends on accurate background separation. Existing software tools such as PPA, CalAtom, and Atomap offer various combinations of denoising and atomic location algorithms, but limitations exist in terms of handling Poisson noise, computational cost, and the ability to extract information from weak signals like light elements. This research introduces a novel strategy to address these limitations.

The literature review extensively covers existing methods for analyzing atomic positions in STEM images. It examines various noise reduction techniques, including image registration and summation, Wiener and band-pass filtering, PCA, non-local means filtering, and BM3D filtering. It also reviews model-based estimation methods that use 2D Gaussian and quadratic functions to fit atomic columns. Furthermore, it discusses several existing software tools that have been developed for atomic resolution image analysis, including Peak Pairs Analysis (PPA), CalAtom, and Atomap. The review highlights their strengths and weaknesses in terms of accuracy, computational cost, and the ability to handle Poisson noise. The authors specifically emphasize the limitations of existing methods in terms of accurately handling Poisson noise and extracting information from weak signals.

The proposed method consists of two main steps: pre-processing for noise reduction and segmented searching for atom positioning. Both high-angle annular dark-field (HAADF) and annular bright-field (ABF) images are utilized to segment atoms. The pre-processing step involves a three-step noise reduction process: (1) noise estimation, which estimates the variance of Gaussian and Poisson noise using a mixed Poisson-Gaussian model; (2) Anscombe transformation to stabilize the variance of Poisson noise and transform it into Gaussian noise; and (3) BM3D filtering to remove the Gaussian noise. Morphological filtering is then applied to remove background stains and bias, followed by histogram stretching to enhance the contrast between atoms and background. The segmentation step employs K-means clustering, an unsupervised learning method, to binarize the image, separating atoms from the background. The coordinates of each atom are then obtained using the center of mass method within the binarized atomic column regions. Heavy atoms are located first using HAADF images, followed by light atoms using ABF images, excluding those already identified in the HAADF image. The entire process is automated within the developed PRESTem software.

The proposed method demonstrates significant improvements in noise reduction and accuracy of atomic position determination. The combination of Anscombe transform, BM3D, and morphological filtering increases the peak signal-to-noise ratio (PSNR) by 8-12 dB compared to the noisy input. Benchmarking against PPA, CalAtom, and Atomap shows that the proposed method achieves sub-pixel precision (average error < 0.7 pixels, corresponding to 4.6 pm), comparable to or better than other methods, while maintaining significantly lower computational cost. The K-means clustering method effectively segments atoms from the background, improving the accuracy of the center of mass method. Applications to simulated SrTiO3 images with varying noise levels show that the method maintains high accuracy even under high noise conditions. The accuracy of structural information obtained using the method is confirmed through analysis of atomic displacement and c/a ratio in perovskite oxide systems, demonstrating that the method is capable of accurate quantitative analysis of local crystal structures at the unit cell scale, achieving errors less than 3 pm in displacement magnitude and less than 4° in displacement angle.

The findings demonstrate the effectiveness of the proposed method in achieving high-precision atomic position determination from noisy STEM images, overcoming challenges posed by limited resolution and noise. The combination of advanced denoising techniques and an unsupervised learning-based segmentation method enables accurate and efficient analysis of atomic structures. The sub-pixel accuracy achieved is crucial for studying subtle structural transitions and mapping materials properties at the picometer scale. The low computational cost compared to other methods makes the proposed approach more practical for large-scale analysis. The application to perovskite systems showcases the potential of the method in understanding complex structure-property relationships in functional materials. Future work could explore the application of the method to other material systems and the integration of more sophisticated machine learning techniques for improved performance.

This study presents a novel method for precise atomic position determination in STEM images using a combination of advanced denoising techniques, unsupervised learning, and a refined center of mass approach. The developed PRESTem software provides an automated and efficient solution for quantitative structural analysis, overcoming limitations of existing methods. The high accuracy and low computational cost make it a powerful tool for studying structure-property relationships in various materials. Future research may focus on integrating more advanced machine learning models and exploring its application to a wider range of materials and imaging modalities.

The study primarily utilizes simulated STEM images for evaluation. While these simulations accurately reflect the noise characteristics of real STEM images, testing on a larger dataset of experimental images is needed to fully validate the method's robustness and generalizability. The method's performance might be affected by factors not explicitly considered in the simulations, such as sample drift, beam damage, or complex interactions between different elements in the material. The current implementation focuses on perovskite structures; further testing is necessary to determine its applicability to other crystal structures and materials with different atomic arrangements.