Nano-Fourier transform infrared (FTIR) imaging is a powerful scanning-based technique at nanometer spatial resolution that combines FTIR spectroscopy and scattering-type scanning near-field optical microscopy (s-SNOM). Recording large spatial areas using nano-FTIR is, however, limited, because its sequential data acquisition entails long measurement times. Compressed sensing and low-rank matrix reconstruction are mathematical techniques that can reduce the number of these measurements significantly by requiring only a small fraction of randomly chosen measurements. However, choosing this small set of measurements in a random fashion poses practical challenges for scanning procedures and does not save as much time as desired. We, therefore, consider different subsampling schemes of practical relevance that ensure rapid data acquisition, much faster than random subsampling, in combination with a low-rank matrix reconstruction procedure. It is demonstrated that the quality of the results for almost all subsampling schemes considered, namely, original Lissajous, triangle Lissajous, and random reflection subsampling, is similar to that achieved for random subsampling. This implies that nano-FTIR imaging can be significantly extended to also cover samples extended over large areas while maintaining its high spatial resolution.
