Three-dimensional stacked filter: A non-linear filter for series images obtained using a transmission electron...

De-noising is an important issue in quantitative high-resolution transmission electron microscopy (HRTEM), and its roles become even more important in applications such as beam-sensitive materials and dynamic characterisations, where the attainable signal-to-noise ratio (SNR) of HRTEM images is frequently limited. In this study, we introduce a three-dimensional stacked filter (3DSF), a novel non-linear filter in which a series of HRTEM images is stacked into a 3D data cube and then treated with the Wiener filter in the 3D domain. In comparison to the traditional Wiener filter, which is widely used for individual images, this filter can accurately estimate the power spectral density of noise and filter images with a higher SNR, fewer artefacts and greater computation efficiency, which works particularly well for HRTEM images containing periodic information and feature similarities in successive micrographs, as demonstrated by simulated and experimental images of graphene and metal-organic framework (MOF). When applied to an ultra-low dose (∼8 e/Ų) HRTEM image stack of MOF MIL-101, the 3DSF could distinguish 40 consecutive frames, revealing the trajectory of subtle lattice shrinkage during the exposure.