  Diffraction tomography is a noninvasive technique that estimates the
refractive indices of unknown objects and involves an inverse-scattering
problem governed by the wave equation. Recent works have shown the benefit of
nonlinear models of wave propagation that account for multiple scattering and
reflections. In particular, the Lippmann-Schwinger~(LiS) model defines an
inverse problem to simulate the wave propagation. Although accurate, this model
is hard to solve when the samples are highly contrasted or have a large
physical size. In this work, we introduce instead a Helmholtz-based nonlinear
model for inverse scattering. To solve the corresponding inverse problem, we
propose a robust and efficient multigrid-based solver. Moreover, we show that
our method is a suitable alternative to the LiS model, especially for strongly
scattering objects. Numerical experiments on simulated and real data
demonstrate the effectiveness of the Helmholtz model, as well as the efficiency
of the proposed multigrid method.
