  Electron backscatter diffraction (EBSD) has developed over the last few
decades into a valuable crystallographic characterisation method for a wide
range of sample types. Despite these advances, issues such as the complexity of
sample preparation, relatively slow acquisition, and damage in beam-sensitive
samples, still limit the quantity and quality of interpretable data that can be
obtained. To mitigate these issues, here we propose a method based on the
subsampling of probe positions and subsequent reconstruction of an incomplete
dataset. The missing probe locations (or pixels in the image) are recovered via
an inpainting process using a dictionary-learning based method called
beta-process factor analysis (BPFA). To investigate the robustness of both our
inpainting method and Hough-based indexing, we simulate subsampled and noisy
EBSD datasets from a real fully sampled Ni-superalloy dataset for different
subsampling ratios of probe positions using both Gaussian and Poisson noise
models. We find that zero solution pixel detection (inpainting un-indexed
pixels) enables higher quality reconstructions to be obtained. Numerical tests
confirm high quality reconstruction of band contrast and inverse pole figure
maps from only 10% of the probe positions, with the potential to reduce this to
5% if only inverse pole figure maps are needed. These results show the
potential application of this method in EBSD, allowing for faster analysis and
extending the use of this technique to beam sensitive materials.
