Denoising atomic resolution 4D scanning transmission electron microscopy data with tensor singular value decomposition.

Tensor singular value decomposition (SVD) is a method to find a low-dimensional representation of data with meaningful structure in three or more dimensions. Tensor SVD has been applied to denoise atomic-resolution 4D scanning transmission electron microscopy (4D STEM) data. On data simulated from a SrTiO [100] perfect crystal and a Si [110] edge dislocation, tensor SVD achieved an average peak signal-to-noise ratio (PSNR) of ~40 dB, which matches or exceeds the performance of other denoising methods, with processing times at least 100 times shorter. On experimental data from SrTiO [100] and LiZnSb [112¯0]/GaSb [110] samples, tensor SVD denoises multiple GB 4D STEM data sets in ten minutes on a typical personal computer. Denoising with tensor SVD improves both convergent beam electron diffraction patterns and virtual-aperture annular dark field images.