Inverse problem in optical tomography and its numerical investigation by iteratively regularized methods

Abstract

It is well known that the diffusion based inverse problem in optical tomography is exponentially ill-posed or unstable, see [2, 18]. In our paper we propose new iteratively regularized numerical methods for the above inverse problem. For the 1D case we compare those methods to MATLAB Levenberg—Marquardt trust region nonlinear least square routine LSQNONLIN both in terms of accuracy and efficiency.