Abstract
We present a framework for optical tomography based on a path integral. Instead of directly solving the radiative transport equations, which have been widely used in optical tomography, we use a path integral that has been developed for rendering participating media based on the volume rendering equation in computer graphics. For a discretized two-dimensional layered grid, we develop an algorithm to estimate the extinction coefficients of each voxel with an interior point method. Numerical simulation results are shown to demonstrate that the proposed method works well.
Highlights
Optical tomography[1,2,3,4,5,6,7,8] is known as a safer alternative to x-ray tomography
Modeling the behavior of light plays an important role in optical tomography, and in the mesoscale, in which the wavelength of light is close to the scale of tissue, the radiative transport equation (RTE) is used for describing the behavior of light scattering.[5,9]
We propose an optical tomography method using path integral as a forward model and solving a nonlinear inverse problem that minimizes the discrepancy between measurements and model predictions in a least-squares sense
Summary
Optical tomography[1,2,3,4,5,6,7,8] is known as a safer alternative to x-ray tomography. The most important application is x-ray computed tomography (CT), where x rays are used due to their penetrative property. There is an urgent demand for a safer medical tomography, such as optical tomography. Modeling the behavior of light plays an important role in optical tomography, and in the mesoscale, in which the wavelength of light is close to the scale of tissue, the radiative transport equation (RTE) is used for describing the behavior of light scattering.[5,9] At the macroscale,[6] the time-independent or dependent RTE is often approximated with a diffusion equation
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