  Optical diffraction tomography (ODT) is an emerging 3D imaging technique that
is used for the 3D reconstruction of the refractive index (RI) for
semi-transparent samples. Various inverse models have been proposed to
reconstruct the 3D RI based on the holographic detection of different samples
such as the Born and the Rytov approximations. However, such approximations
usually suffer from the so-called missing-cone problem that results in an
elongation of the final reconstruction along the optical axis. Different
iterative schemes have been proposed to solve the missing cone problem relying
on physical forward models and an error function that aims at filling in the
k-space and thus eliminating the missing-cone problem and reaching better
reconstruction accuracy. In this paper, we propose a different approach where a
3D neural network (NN) is employed. The NN is trained with a cost function
derived from a physical model based on the physics of optical wave propagation.
The 3D NN starts with an initial guess for the 3D RI reconstruction (i.e. Born,
or Rytov) and aims at reconstructing better 3D reconstruction based on an error
function. With this technique, the NN can be trained without any examples of
the relation between the ill-posed reconstruction (Born or Rytov) and the
ground truth (true shape).
