  We develop a new retrieval scheme for obtaining two-dimensional surface maps
of exoplanets from scattered light curves. In our scheme, the combination of
the L1-norm and Total Squared Variation, which is one of the techniques used in
sparse modeling, is adopted to find the optimal map. We apply the new method to
simulated scattered light curves of the Earth, and find that the new method
provides a better spatial resolution of the reconstructed map than those using
Tikhonov regularization. We also apply the new method to observed scattered
light curves of the Earth obtained during the two-year DSCOVR/EPIC observations
presented by Fan et al. (2019). The method with Tikhonov regularization enables
us to resolve North America, Africa, Eurasia, and Antarctica. In addition to
that, the sparse modeling identifies South America and Australia, although it
fails to find the Antarctica maybe due to low observational weights on the
poles. Besides, the proposed method is capable of retrieving maps from noise
injected light curves of a hypothetical Earth-like exoplanet at 5 pc with noise
level expected from coronagraphic images from a 8-m telescope. We find that the
sparse modeling resolves Australia, Afro-Eurasia, North America, and South
America using 2-year observation with a time interval of one month. Our study
shows that the combination of sparse modeling and multi-epoch observation with
1 day or 5 days per month can be used to identify main features of an Earth
analog in future direct imaging missions such as the Large UV/Optical/IR
Surveyor (LUVOIR).
