While aberration correction for scanning transmission electron microscopes (STEMs) dramatically increased the spatial resolution obtainable in the images of materials that are stable under the electron beam, the practical resolution of many STEM images is now limited by the sample stability rather than the microscope. To extract physical information from the images of beam sensitive materials, it is becoming clear that there is a critical dose/dose-rate below which the images can be interpreted as representative of the pristine material, while above it the observation is dominated by beam effects. Here, we describe an experimental approach for sparse sampling in the STEM and in-painting image reconstruction in order to reduce the electron dose/dose-rate to the sample during imaging. By characterizing the induction limited rise-time and hysteresis in the scan coils, we show that a sparse line-hopping approach to scan randomization can be implemented that optimizes both the speed of the scan and the amount of the sample that needs to be illuminated by the beam. The dose and acquisition time for the sparse sampling is shown to be effectively decreased by at least a factor of 5× relative to conventional acquisition, permitting imaging of beam sensitive materials to be obtained without changing the microscope operating parameters. The use of sparse line-hopping scan to acquire STEM images is demonstrated with atomic resolution aberration corrected the Z-contrast images of CaCO3, a material that is traditionally difficult to image by TEM/STEM because of dosage issues.