A Variable Density Sampling Scheme for Compressive Fourier Transform Interferometry

Fourier transform interferometry (FTI) is an appealing hyperspectral (HS) imaging modality for many applications demanding high spectral resolution, e.g., in fluorescence microscopy. However, the effective resolution of FTI is limited by the durability of biological elements when exposed to illuminating light. Overexposed elements are indeed subject to photo-bleaching and become unable to fluoresce. In this context, the acquisition of biological HS volumes based on sampling the optical path difference axis at Nyquist rate leads to unpleasant trade-offs between spectral resolution, quality of the HS volume, and light exposure intensity. In this paper we propose two variants of the FTI imager, i.e., coded illumination-FTI (CI-FTI) and structured illumination FTI (SI-FTI), based on the theory of compressive sensing (CS). These schemes efficiently modulate light exposure temporally (in CI-FTI) or spatiotemporally (in SI-FTI). Leveraging a variable density sampling strategy recently introduced in CS, we provid...