Local low rank denoising for enhanced atomic resolution imaging

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.