  Just as turbulence in the Earth's atmosphere can severely limit the angular
resolution of optical telescopes, turbulence in the ionized interstellar medium
fundamentally limits the resolution of radio telescopes. We present a
scattering mitigation framework for radio imaging with very long baseline
interferometry (VLBI) that partially overcomes this limitation. Our framework,
"stochastic optics," derives from a simplification of strong interstellar
scattering to separate small-scale ("diffractive") effects from large-scale
("refractive") effects, thereby separating deterministic and random
contributions to the scattering. Stochastic optics extends traditional
synthesis imaging by simultaneously reconstructing an unscattered image and its
refractive perturbations. Its advantages over direct imaging come from
utilizing the many deterministic properties of the scattering -- such as the
time-averaged "blurring," polarization independence, and the deterministic
evolution in frequency and time -- while still accounting for the stochastic
image distortions on large scales. These distortions are identified in the
image reconstructions through regularization by their time-averaged power
spectrum. Using synthetic data, we show that this framework effectively removes
the blurring from diffractive scattering while reducing the spurious image
features from refractive scattering. Stochastic optics can provide significant
improvements over existing scattering mitigation strategies and is especially
promising for imaging the Galactic Center supermassive black hole, Sagittarius
A*, with the Global mm-VLBI Array and with the Event Horizon Telescope.
