Application of transform algorithms to high-resolution image reconstruction in optical diffusion tomography of strongly scattering media

Abstract

The applicability of transform algorithms generally used in projection-computed tomography is substantiated for the case of medical optical diffusion tomography (ODT). To reconstruct tissue optical inhomogeneities, a new method based on a concept of an average statistical trajectory for transfer of light energy [photon average trajectory (PAT)] is proposed. By this method, the inverse problem of ODT is reduced to a solution of an integral equation with integration along a PAT. Within the internal zone of the object, well away from the boundaries, PATs tend to a straight line, and standard integral algorithms based on the inverse Radon transform may be used to restore diffuse optical images. To demonstrate the capabilities of the PAT method, a numerical experiment on cross sectional reconstruction of cylindrical strongly scattering objects with low-contrast absorbing inhomogeneities is conducted. To solve the time-domain ODT inverse problem, two filtered backprojection algorithms (of Radon and Vainberg) are used. The reconstruction results are compared with those obtained by a well-known software package for temporal optical absorption and scattering tomography, based on multiple solutions of a diffusion equation. It is shown that in important cases of low-contrast absorbing inhomogeneities, the PAT method using the Vainberg algorithm allows reconstruction of tissue optical inhomogeneities with a 20% gain in spatial resolution.