Adaptive nonlinear multigrid inversion with applications to Bayesian optical diffusion tomography

We previously proposed a general framework for nonlinear multi-grid inversion applicable to any inverse problem in which the forward model can be naturally represented at differing resolutions. The method has the potential for very large computational savings and robust convergence. In this paper, multigrid inversion is further extended to adaptively allocate computation to the scale at which the algorithm can best reduce the cost. We applied the proposed method to solve the problem of optical diffusion tomography in a Bayesian framework, and our simulation results indicate that the adaptive scheme can improve computational efficiency in this application.