Layered optical tomography of multiple scattering media with combined constraint optimization

Abstract

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.

Optical tomography with discretized path integral

“…(28)] to estimate the extinction coefficients of the 2-D layered model. As we mentioned before, we fix the light paths and assume that the scattering coefficients and parameters of the Gaussian phase function are uniform and known in advance.…”

“…This paper is an extension of our previous conference version 27,28 with additional theoretical background and additional experiments and discussions, and is structured as follows. In Sec.…”

Primal-dual approach to optical tomography with discretized path integral with efficient formulations

“…In contrast to x-ray computed tomography, which uses x-rays instead of light, safer tomographic methods are demanded and scattering optical tomography methods are recently attracting computer vision researchers’ attention. 9 – 15 …”

“…We investigate a recently proposed optical tomography with discretized path integral. 12 , 13 , 15 Their method takes advantages of the path integral formulation and formulates the inverse problem of optical tomography as a constraint nonlinear least squared optimization problem. This method benefits from various optimization techniques, which is not the case for voting 11 , 14 or genetic algorithms.…”

“… 16 Second, we propose new formulations of equations. The main bottle-neck of the previous approaches 12 , 13 , 15 is Jacobian and Hessian which are computationally demanding as the number of paths increases. Our new formulations are equivalent to the previous ones, but much more efficient.…”