Joint denoising and line distortion correction for raster-scanned image series

TL;DR

This work tackles noise and line distortions in raster-scanned image series, focusing on STEM/HAADF data where sampling is distorted by beam-position jitter and drift. It develops a multi-frame variational framework that jointly denoises and corrects distortions by estimating a set of frame-specific distortions $\phi_k$ while recovering a common underlying image $f$, through regularized losses that combine data fidelity $\operatorname{Dist}_{\text{dat}}$ and operator regularization $\operatorname{Dist}_{\text{op}}$, with a noise model leading to $\operatorname{Dist}_{\text{dat}}(u,v)=u-v\log u$ under Poisson statistics. The paper surveys five modeling approaches, including pairwise and global regularization schemes, a non-rigid registration method (Smart Align), a Bayesian bump-fit denoising model, and a new spline-based image model, each providing distinct initialization and optimization strategies. Numerical results on synthetic and real HAADF-STEM data demonstrate that the spline-based joint denoising method (JUD) achieves competitive atom localization precision and superior intensity reconstruction, with favorable scaling as the number of frames grows. Overall, the work advances robust, motion-aware reconstruction for high-resolution raster-scanned imaging, enabling more accurate material characterization from STEM data.

Abstract

The problem of noise in a general data acquisition procedure can be resolved more accurately if it is based on a model that describes well the distortions of the data including both spatial and intensity changes. The focus of this article is the modeling of the position distortions during sequential data acquisitions. A guiding example is the data obtained by Scanning Transmission Electron Microscopy (STEM) and High Angular Annular Dark Field (HAADF) data, in particular. The article discusses different models of the position noise and their numerical implementations comparing some computational results.

Figures (6)

• Figure 1: First and last image of the synthetic STEM images series used for the numerical performance evaluation.
• Figure 3: Distances used to compute the precision in $x$ and $y$-direction.
• Figure 4: Left: Precision plot for the synthetic test data set for different methods. The horizontal axis shows the number of images used for the reconstruction, the vertical axis the precision value in picometer. Right: Estimated atom sizes in pixels for a synthetic test data set.
• Figure 5: Ground truth image the synthetic STEM image series was created from and the three reconstructions obtained with the different methods using the whole series of 64 images.
• Figure 7: Precision plot for the HAADF STEM GaN $[11\overline{2}0]$ image series.