Event-sparse stack denoising for 4D-STEM applications

TL;DR

The paper tackles noise in low-dose 4D-STEM by introducing event-sparse stack denoising (sparse-stack denoising) and the locally time-resolved STEM (LTR-STEM) acquisition, which collects multiple sparse diffraction patterns per scan position. Two denoising pipelines are developed: a DBSCAN-based clustering approach with a two-stage soft/hard threshold and a sparse PCA-based decomposition with a single reconstructed component. Across simulations and experiments, the methods yield higher PSNR than noisy reconstructions, achieving similar image quality with ~16% of the exposure, and substantially improving defect-detection sensitivity (e.g., 4.1× in radial disk-shift detection). The LTR-STEM framework also enables exposure-selective imaging and quantitative dose estimation, demonstrating practical avenues for low-dose, high-fidelity 4D-STEM analyses, with pipeline efficiency and future gains anticipated from event-based detectors.

Abstract

We introduce a denoising method for four-dimensional scanning transmission electron microscopy (4D-STEM) 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 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 diffraction data denoising, as shown by simulated peak signal-to-noise ratio (PSNR) curves, denoised experimental data for virtual imaging, and application-specific denoising for defect detection. PSNR analysis indicates that sparsity-denoised 4D-STEM data reaches the same PSNR as raw data at approximately 16% of the exposure time, demonstrating comparable image quality with a lower dose. In defect detection, a 4.1x 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.

Figures (6)

• Figure 1: Visualization of the denoising process, showing the acquired diffraction pattern stack (LTR-STEM), the denoising procedures applied to the stack, and the resulting denoised diffraction pattern.
• Figure 2: Event-sparse stack denoising of simulated diffraction data with PSNR quantification of the denoised results. a) PSNR curves of noisy data and denoised data obtained using the DBSCAN algorithm (clustering) and the sparse PCA algorithm (decomposition). The blue dashed line marks the point (x = 31) where the PSNR of the clustering-based denoising equals that of the noisy data reconstructed using all 200 components. b) Example diffraction pattern from the stack with added Poisson noise. c,g) Ground truth stack sums before noise addition, using 10 and 200 images, respectively. d,h) Corresponding stack sums with added Poisson noise. e,i) Results of clustering-based denoising. f,j) Results of sparse PCA denoising.
• Figure 3: Application of sparse-stack denoising to virtual imaging of nanocrystalline Au. a–c) VDF images from the raw data, clustering-denoised data, and sparse PCA–denoised data using ROI1. d–f) Corresponding VDF images using ROI2. g–i) Mean diffraction patterns with aperture positions indicated.
• Figure 4: Sparse-stack denoising applied to individual diffraction patterns from the Au dataset. a,e) Single raw patterns. b,f) Summed pattern stacks. c,g) DBSCAN-denoised patterns. d,h) Sparse PCA–denoised patterns. i) Line profiles across a Bragg disk row comparing raw and denoised intensities.
• Figure 5: Application of sparse-stack denoising to virtual imaging and defect identification in guanine nanocrystallites. a–c) VDF images from the (100) reflection: a) raw data; b–c) denoised results from the DBSCAN algorithm with increasing $\text{min}\_\text{samples}$ values, leading to greater noise reduction. d–f) Corresponding center-of-mass radial disk-shift maps: d) raw data; e–f) denoised results with progressively higher $\text{min}\_\text{samples}$ values. Line profiles across a defect-containing region, extracted from d–f), are plotted in g). h–j) Diffraction patterns from the crystalline region highlighted in a–c), cropped around the (100) reflection row: h) raw data; i–j) denoised results with increasing $\text{min}\_\text{samples}$ values. Diffraction patterns have been rotated by 49° counterclockwise for visualization. The (100) reflection used for VDF reconstruction and radial shift measurement is marked by red dotted circles. Inner and outer circles indicate the regions used for SNR calculation, with values reported in h–j).