  The problem of reconstructing an object from the measurements of the light it
scatters is common in numerous imaging applications. While the most popular
formulations of the problem are based on linearizing the object-light
relationship, there is an increased interest in considering nonlinear
formulations that can account for multiple light scattering. In this paper, we
propose an image reconstruction method, called CISOR, for nonlinear diffractive
imaging, based on a nonconvex optimization formulation with total variation
(TV) regularization. The nonconvex solver used in CISOR is our new variant of
fast iterative shrinkage/thresholding algorithm (FISTA). We provide fast and
memory-efficient implementation of the new FISTA variant and prove that it
reliably converges for our nonconvex optimization problem. In addition, we
systematically compare our method with other state-of-the-art methods on
simulated as well as experimentally measured data in both 2D and 3D settings.
