Nonlinear multigrid algorithms for Bayesian optical diffusion tomography

Optical diffusion tomography is a technique for imaging a highly scattering medium using measurements of transmitted modulated light, Reconstruction o f the spatial distribution of the optical properties of the medium from suc h data is a difficult nonlinear inverse problem. Bayesian approaches are ef fective, but are computationally expensive, especially for three-dimensiona l (3-D) imaging. This paper presents a general nonlinear multigrid optimiza tion technique suitable for reducing the computational burden in a range of nonquadratic optimization problems. This multigrid method is applied to co mpute 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 reconst ructed image quality.