Assessment of Subsampling Schemes for Compressive Nano-FTIR Imaging

Abstract

Nano-FTIR imaging is a powerful scanning-based technique at nanometer spatial resolution that combines Fourier transform infrared spectroscopy (FTIR) 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 sub-sampling schemes of practical relevance that ensure rapid data acquisition, much faster than random sub-sampling, in combination with a low-rank matrix reconstruction procedure. It is demonstrated that the quality of the results for almost all sub-sampling schemes considered, namely original Lissajous, triangle Lissajous, and random reflection sub-sampling, is similarly to that achieved for random sub-sampling. This implies that nano-FTIR imaging can be significantly extended to also cover samples extended over large areas while maintaining its high spatial resolution.