  Nano-FTIR imaging is a powerful scanning-based technique at nanometer spatial
resolution which combines Fourier transform infrared spectroscopy (FTIR) and
scattering-type scanning near-field optical microscopy (s-SNOM). However,
recording large spatial areas with nano-FTIR is limited by long measurement
times due to its sequential data acquisition. Several mathematical approaches
have been proposed to tackle this problem. All of them have in common that only
a small fraction of randomly chosen measurements is required.
  However, choosing the fraction of measurements in a random fashion poses
practical challenges for scanning procedures and does not lead to time savings
as large as desired. We consider different, practically relevant sub-sampling
schemes assuring a faster acquisition. It is demonstrated that results for
almost all considered sub-sampling schemes, namely original Lissajous, triangle
Lissajous, and random reflection sub-sampling, at a sub-sampling rate of 10%,
are comparable to results when using a random sub-sampling of 10%. This implies
that random sub-sampling is not required for efficient data acquisition.
