  We investigate the ability to reconstruct and derive spatial structure from
sparsely sampled 3D piezoresponse force microcopy data, captured using the
band-excitation (BE) technique, via Gaussian Process (GP) methods. Even for
weakly informative priors, GP methods allow unambiguous determination of the
characteristic length scales of the imaging process both in spatial and
frequency domains. We further show that BE data set tends to be oversampled,
with ~30% of the original data set sufficient for high-quality reconstruction,
potentially enabling the faster BE imaging. Finally, we discuss how the GP can
be used for automated experimentation in SPM, by combining GP regression with
non-rectangular scans. The full code for GP regression applied to hyperspectral
data is available at https://git.io/JePGr.
