  This paper introduces a single-pixel HyperSpectral (HS) imaging framework
based on Fourier Transform Interferometry (FTI). By combining a space-time
coding of the light illumination with partial interferometric observations of a
collimated light beam (observed by a single pixel), our system benefits from
(i) reduced measurement rate and light-exposure of the observed object compared
to common (Nyquist) FTI imagers, and (ii) high spectral resolution as desirable
in, e.g., Fluorescence Spectroscopy (FS). From the principles of compressive
sensing with multilevel sampling, our method leverages the sparsity "in level"
of FS data, both in the spectral and the spatial domains. This allows us to
optimize the space-time light coding using time-modulated Hadamard patterns. We
confirm the effectiveness of our approach by a few numerical experiments.
