Optics and Inverse Problems: Optical Tomography

Abstract

Optical tomography is one of medical imaging modalities such as X-ray CT, ultrasound, and MRI. Near-infrared light is used because light in this range of wavelength is absorbed relatively weakly in biological tissue. Such light, however, is strongly scattered in biological tissue and the specific intensity of light obeys the radiative transport equation, which is a linear Boltzmann equation. Optical tomography is formulated as an inverse problem of determining coefficients of the radiative transport equation from boundary measurements. Since it is difficult to solve the radiative transport equation analytically and even numerically, the radiative transport equation is usually approximated by the diffusion equation. As one can easily imagine, the use of this diffusion approximation results in low resolution of reconstructed images. Recent progress in this field makes it possible to obtain tomographic images using the radiative transport equation without relying on the diffusion approximation.