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We investigate the ability to reconstruct and derive spatial structure fromsparsely sampled 3D piezoresponse force microcopy data, captured using theband-excitation (BE) technique, via Gaussian Process (GP) methods. Even forweakly informative priors, GP methods allow unambiguous determination of thecharacteristic length scales of the imaging process both in spatial andfrequency 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 canbe used for automated experimentation in SPM, by combining GP regression withnon-rectangular scans. The full code for GP regression applied to hyperspectraldata is available at https://git.io/JePGr.

Imaging Mechanism for Hyperspectral Scanning Probe Microscopy via Gaussian Process Modelling