Millane, “Nonlinear multigrid algorithms for Bayesian optical diffusion tomography

Abstract — Optical diffusion tomography is a technique for imaging a highly scattering medium using measurements of the transmitted modulated light. Reconstruction of the spatial distribution of the optical properties of the medium from such data is a very difficult nonlinear inverse problem. Bayesian approaches are effective, but are computationally expensive, especially for three-dimensional imaging. This paper presents a general nonlinear multigrid optimization technique suitable for reducing the computational burden in a range of non-quadratic optimization problems. This multigrid method is applied to compute the maximum a posteriori (MAP) estimate of the reconstructed image in the optical diffusion tomography problem. The proposed multigrid approach both dramatically reduces the required computation and improves the reconstructed image quality