  The time series of light reflected from exoplanets by future direct imaging
can provide spatial information with respect to the planetary surface. We apply
sparse modeling to the retrieval method that disentangles the spatial and
spectral information from multi-band reflected light curves termed as
spin-orbit unmixing. We use the $\ell_1$-norm and the Total Squared Variation
norm as regularization terms for the surface distribution. Applying our
technique to a toy model of cloudless Earth, we show that our method can infer
sparse and continuous surface distributions and also unmixed spectra without
prior knowledge of the planet surface. We also apply the technique to the real
Earth data as observed by DSCOVR/EPIC. We determined the representative
components that can be interpreted as cloud and ocean. Additionally, we found
two components that resembled the distribution of land. One of the components
captures the Sahara Desert, and the other roughly corresponds to vegetation
although their spectra are still contaminated by clouds. Sparse modeling
significantly improves the geographic retrieval, in particular, of cloud and
leads to higher resolutions for other components when compared with spin-orbit
unmixing using Tikhonov regularization.
