  Seeing oceans, continents, quasi-static weather, and other surface features
on exoplanets may allow us to detect and characterize life outside the solar
system. The Proxima b planet resides within the stellar habitable zone allowing
for liquid water on its surface, and it may be Earth-like. However, even the
largest planned telescopes will not be able to resolve its surface features
directly. Here, we demonstrate an inversion technique to image indirectly
exoplanet surfaces using observed unresolved reflected light variations over
the course of the exoplanets orbital and axial rotation: ExoPlanet Surface
Imaging (EPSI). We show that the reflected light curve contains enough
information to detect both longitudinal and latitudinal structures and to map
exoplanet surface features. We demonstrate this using examples of Solar system
planets and moons as well as simulated planets with Earth-like life and
artificial megastructures. We also describe how it is possible to infer the
planet and orbit geometry from light curves. In particular, we show how albedo
maps of Proxima b can be successfully reconstructed for tidally locked,
resonance, and unlocked axial and orbital rotation. Such albedo maps obtained
in different wavelength passbands can provide "photographic" views of distant
exoplanets. We estimate the signal-to-noise ratio necessary for successful
inversions and analyse telescope and detector requirements necessary for the
first surface images of Proxima b and other nearby exoplanets.
