Local low rank denoising for enhanced atomic resolution imaging

Highlights: • Local low rank denoising is introduced for noisy images and spectrum images. • LLR enables accurate denoising also of spatially complex samples. • Using LLR row wise distortion in STEM images are visualized. • EELS maps of Co2FeO4 are drastically improved by applying LLR. - Abstract: Atomic resolution imaging and spectroscopy suffers from inherently low signal to noise ratios often prohibiting the interpretation of single pixels or spectra. We introduce local low rank (LLR) denoising as tool for efficient noise removal in scanning transmission electron microscopy (STEM) images and electron energy-loss (EEL) spectrum images. LLR denoising utilizes tensor decomposition techniques, in particular the multilinear singular value decomposition (MLSVD), to achieve a denoising in a general setting largely independent of the signal features and data dimension, by assuming that the signal of interest is of low rank in segments of appropriately chosen size. When applied to STEM images of graphene, LLR denoising suppresses statistical noise while retaining fine image features such as scan row-wise distortions, possibly related to rippling of the graphene sheet and consequent motion of atoms. When applied to EEL spectra, LLR denoising reveals fine structures distinguishing different lattice sites in the spinel system CoFe₂O₄.