Understanding greenhouse gas fluxes at the Earth’s surface is becoming crucial in the context of climate change. The aim of the CNES/UKSA MicroCarb mission is therefore to map, on a planetary scale, the sources and sinks of carbon, the main greenhouse gas in the atmosphere. To do this, a spectrometer will be sent in space to acquire spectra in 4 narrow bands around wavelengths associated with O2 and CO2. However, measurement errors can occur due to the instrument used, and induce errors in the resulting trace gas concentrations. It is therefore crucial to estimate the spectral response of the instrument as accurately as possible. This paper investigates a new estimation method for this spectral response that uses a sparse representation in a dictionary of appropriate basis functions. This sparse representation is performed using the LASSO and Orthogonal Matching Pursuit (OMP) algorithms. Simulations conducted on data mimicking observations resulting from the MicroCarb instrument allow the performance of this method to be appreciated.