LoRePIE: ℓ₀ regularized extended ptychographical iterative engine for low-dose and fast electron ptychography

The extended Ptychographical Iterative Engine (ePIE) is a widely used phase retrieval algorithm for electron ptychography from 4-dimensional (4-D) ccanning transmission electron microscopy (4-D STEM) measurements acquired with a focused or defocused electron probe. However, ePIE relies on redundancy in the data and hence requires adjacent illuminated areas to overlap. In this paper, we propose a regularized variant of ePIE that is more robust to low overlap ratios. We examine the performance of the proposed algorithm on an experimental 4-D STEM data of double layered Rotavirus particles acquired in a full scan with 85% overlap. By artificial down-sampling of the probe positions, we have created synthetic 4-D STEM datasets with different overlap ratios and use these to show that a high quality reconstruction of Rotavirus particles can be obtained from data with an overlap as low as 56%.