Application of integral transform algorithms to high-resolution reconstruction of tissue inhomogeneities in medical diffuse optical tomography

The applicability of the transform algorithms generally used in projection computed tomography is substantiated for the case of medical diffuse optical tomography (DOT). 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 DOT is reduced to solution of integral equation with integration along a PAT. Within the internal zone of the object, remote 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 absorbing inhomogeneities has been conducted. To solve the DOT inverse problem, two filtered backprojection algorithms (of Radon and of Vainberg) were 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 solution of diffusion equation. It is shown that the PAT method using the Vainberg algorithm allows reconstruction of tissue optical structure with a 20%-gain in spatial resolution.