Traditional image acquisition for cryo focused ion-beam scanning electron microscopy (FIB-SEM) tomography often sees thousands of images being captured over a period of many hours, with immense data sets being produced. When imaging beam sensitive materials, these images are often compromised by additional constraints related to beam damage and the devitrification of the material during imaging, which renders data acquisition both costly and unreliable. Subsampling and inpainting are proposed as solutions for both of these aspects, allowing fast and low-dose imaging to take place in the Focused ion-beam scanning electron microscopy FIB-SEM without an appreciable loss in image quality. In this work, experimental data are presented which validate subsampling and inpainting as a useful tool for convenient and reliable data acquisition in a FIB-SEM, with new methods of handling three-dimensional data being employed in the context of dictionary learning and inpainting algorithms using a newly developed microscope control software and data recovery algorithm.