Framework of compressive sensing and data compression for 4D-STEM

Four-dimensional Scanning Transmission Electron Microscopy (4D-STEM) is a powerful technique for highresolution and high-precision materials characterization at multiple length scales, including the characterization of beam-sensitive materials. However, the field of view of 4D-STEM is relatively small, which in absence of live processing is limited by the data size required for storage. Furthermore, the rectilinear scan approach currently employed in 4D-STEM places a resolution- and signal-dependent dose limit for the study of beam sensitive materials. Improving 4D-STEM data and dose efficiency, by keeping the data size manageable while limiting the amount of electron dose, is thus critical for broader applications. Here we introduce a general method for reconstructing 4D-STEM data with subsampling in both real and reciprocal spaces at high fidelity. The approach is first tested on the subsampled datasets created from a full 4D-STEM dataset, and then demonstrated experimentally using random scan in real-space. The same reconstruction algorithm can also be used for compression of 4D-STEM datasets, leading to a large reduction (100 times or more) in data size, while retaining the fine features of 4D-STEM imaging, for crystalline samples.