Multigrid Inversion Algorithms with Applications to Optical Diffusion Tomography

In this paper, we propose a general framework for nonlinear multigrid inversion applicable to any inverse problem in which the forward model can be naturally represented at di#ering resolutions. In multigrid inversion, the problem is adjusted to be solved at each resolution by using the solutions at both finer and coarser resolutions. To do this, we formulate a consistent set of cost functionals across resolutions. At each resolution, both the forward and inverse problems are discretized at the lower resolution; thus reducing computation. Our simulation results for the problem of optical di#usion tomography indicate that multigrid inversion can dramatically reduce computation in this application