Layered optical tomography of multiple scattering media with combined constraint optimization

In this paper, we proposed an improved optical scattering tomography for optically dense media. We model a material by many layers with voxels, and light scattering by a distribution from a voxel in one layer to other voxels in the next layer. Then we write attenuation of light along a light path by an inner product of vectors, and formulate the scattering tomography as an inequality constraint optimization problem solved by an interior point method. To improve the accuracy, we solve simultaneously four configurations of a multiple-scattering tomography, however, this would increase the computational cost by a factor of four if we simply solved the problem four times. To reduce the computation cost, we introduce a quasi-Newton method to update the inverse of a Hessian matrix used in the iteration of the interior point method. We show experimental results with numerical simulation for evaluating the proposed method and comparisons with our previous work.