Ptychography is a powerful imaging technique that is used in a variety of fields, including materials science, biology, and nanotechnology. However, the accuracy of the reconstructed ptychography image is highly dependent on the accuracy of the recorded probe positions which often contain errors. These errors are typically corrected jointly with phase retrieval through numerical optimization approaches. When the error accumulates along the scan path or when the error magnitude is large, these approaches may not converge with satisfactory result. We propose a fundamentally new approach for ptychography probe position prediction for data with large position errors, where a neural network is used to make single-shot phase retrieval on individual diffraction patterns, yielding the object image at each scan point. The pairwise offsets among these images are then found using a robust image registration method, and the results are combined to yield the complete scan path by constructing and solving a linear equation. We show that our method can achieve good position prediction accuracy for data with large and accumulating errors on the order of $10^2$ pixels, a magnitude that often makes optimization-based algorithms fail to converge. For ptychography instruments without sophisticated position control equipment such as interferometers, our method is of significant practical potential.

Cryo Focused Ion-Beam Scanning Electron Microscopy (cryo FIB-SEM) enables three-dimensional and nanoscale imaging of biological specimens via a slice and view mechanism. The FIB-SEM experiments are, however, limited by a slow (typically, several hours) acquisition process and the high electron doses imposed on the beam sensitive specimen can cause damage. In this work, we present a compressive sensing variant of cryo FIB-SEM capable of reducing the operational electron dose and increasing speed. We propose two Targeted Sampling (TS) strategies that leverage the reconstructed image of the previous sample layer as a prior for designing the next subsampling mask. Our image recovery is based on a blind Bayesian dictionary learning approach, i.e., Beta Process Factor Analysis (BPFA). This method is experimentally viable due to our ultra-fast GPU-based implementation of BPFA. Simulations on artificial compressive FIB-SEM measurements validate the success of proposed methods: the operational electron dose can be reduced by up to 20 times. These methods have large implications for the cryo FIB-SEM community, in which the imaging of beam sensitive biological materials without beam damage is crucial.