An inverse scattering problem to reconstruct refractive index distributions

Optical tomography is used for noninvasive imaging of biological samples in microscopy. Light propagation in complex media is a difficult process to analyze and control. A key challenge is to identify a significant parameter which describes the inhomogeneous scattering in tissue, called the refractive index. In literature it has been shown numerically that one can reconstruct the refractive index distribution via a beam propagation model and convex optimization. Major obstacles for accurate reconstruc- tion are an increasing sample depth and a limited field of view. Hence, it is essential to tackle the ill-posedness and nonlinear dependence in the refractive index estimation. This thesis introduces regularized variational methods for the non-convex refractive index estima- tion problem. To achieve accurate reconstructions, state-of-the-art stochastic and non-convex splitting methods are introduced for this problem and compared in realistic numerical simulations.