Event-sparse stack denoising for 4D-STEM applications

We introduce a denoising method for four-dimensional scanning transmission electron microscopy (4D-STEM) for Bragg diffraction analysis that relies on processing local, scan position-independent electron event-sparse data stacks, called event-sparse stack denoising. This method adds an extra time dimension during data collection by recording multiple electron event-sparse nanobeam diffraction patterns. The resulting datasets are effectively five-dimensional, referred to as locally time-resolved STEM (LTR-STEM). Diffraction data stacks at each scan position are processed using one of two sparsity denoising pipelines: (1) the density-based spatial clustering of applications with noise (DBSCAN) algorithm followed by multi-step persistence thresholding, or (2) sparse principal component analysis (sparse PCA), followed by single-step thresholding. Both methods perform well for nanobeam diffraction data denoising, as shown by simulated signal-to-noise ratio (SNR) and recall curves, denoised experimental data for virtual imaging, and application-specific denoising for defect detection. SNR analysis of diffraction signal indicates that sparsity-denoised 4D-STEM data reaches the same SNR as raw data at approximately 38.5% of the exposure time, demonstrating comparable image quality with a lower dose. In defect detection, a 4.1× increase in sensitivity to relative radial disk shift is observed in the denoised data. Moreover, the LTR-STEM technique may be used to inspect material degradation by tracking changes in diffraction disk intensity, allowing for critical dose estimation and exposure-selective imaging.