Nonlinear multigrid optimization for Bayesian diffusion tomography
Optical diffusion tomography attempts to reconstruct an object cross section from measurements of scattered and attenuated light. While Bayesian approaches are well suited to this difficult nonlinear inverse problem, the resulting optimization problem is very computationally expensive. In this paper, we propose a nonlinear multigrid technique for computing the maximum a posteriori (MAP) reconstruction in the optical diffusion tomography problem. The multigrid approach improves reconstruction quality by avoiding local minimum. In addition, it dramatically reduces computation. Each iteration of the algorithm alternates a Born approximation step with a single cycle of a nonlinear multigrid algorithm.