Error-Guaranteed Compression with Preservation of Downstream Quantities for Electron MicroscopyȠ

Recent electron microscopy workflows, particularly 4D Scanning Transmission Electron Microscopy (4D STEM), generate massive data volumes, sometimes exceeding tens of terabytes per dataset. This growth is outpacing improvements in storage, network, and I/O bandwidths. Although lossless compression offers a viable solution, it is often limited by modest compression ratios. Lossy compression offers an alternative; however, compression errors can propagate to downstream analyses. The goal is therefore to deploy a compression method that preserves essential data features while defining a suitable metric. In this paper, we present a moment-preserving compression workflow combining multigrid adaptive reduction (MGARD) with a constraint satisfaction technique. MGARD provides mathematically guaranteed error bounds on raw data, while a constraint satisfaction method rectifies decompressed data to strictly preserve selected statistical moments in diffraction space. This allows moment-derived observables, such as Center-of-Mass (COM) measurements, to be recovered consistently from the corrected tensor. Furthermore, we propose a frequency-domain reliability criterion in raw diffraction space to evaluate the acceptable accuracy limits. Experiments on 4D STEM datasets demonstrate that this moment-preserving adjustment substantially reduces errors in targeted downstream quantities, providing a practical path toward compressed 4D STEM data compatible with downstream microscopy analysis.