  We describe an approach based on compressive-sampling which allows for a
considerable reduction in the acquisition time in Fourier-transform
spectroscopy. In this approach, an N-point Fourier spectrum is resolved from
much less than N time-domain measurements using a compressive-sensing
reconstruction algorithm. We demonstrate the technique by resolving sparse
vibrational spectra using <25% of the Nyquist rate samples in single-pulse CARS
experiments. The method requires no modifications to the experimental setup and
can be directly applied to any Fourier-transform spectroscopy measurement, in
particular multidimensional spectroscopy.
