  Despite advancements in electron backscatter diffraction (EBSD) detector
speeds, the acquisition rates of 4-Dimensional (4D) EBSD data, i.e., a
collection of 2-dimensional (2D) diffraction maps for every position of a
convergent electron probe on the sample, is limited by the capacity of the
detector. Such 4D data enables computation of, e.g., band contrast and Inverse
Pole Figure (IPF) maps, used for material characterisation. In this work we
propose a fast acquisition method of EBSD data through subsampling 2-D probe
positions and inpainting. We investigate reconstruction of both band contrast
and IPF maps using an unsupervised Bayesian dictionary learning approach, i.e.,
Beta process factor analysis. Numerical simulations achieve high quality
reconstructed images from 10% subsampled data.
