  Broadband, high resolution and rapid measurement of dual-comb spectroscopy
(DCS) generates a large amount of data stream. We numerically demonstrate
significant data compression of DCS spectra by using a compressive sensing
technique. Our numerical simulation shows a compression rate of more than 100
with 3% error in mole fraction estimation of mid-infrared (MIR) DCS of two
molecular species in a broadband (~30 THz) and high resolution (~115 MHz)
condition. We also numerically demonstrate a massively parallel MIR DCS
spectrum of 10 different molecular species can be reconstructed with a
compression rate of 10.5 with a transmittance error of 0.003 from the original
spectrum.
