An algorithm for recovering the absorption coefficient from reflected light using a discrete diffusion model

An algorithm based on a discrete model for photon migration is proposed for recovering the absorption coefficient in a semi-infinite slab. A pulsed light source is modelled and only reflected signals are used in the reconstruction. It is assumed that the diffusion coefficient and the speed of light are both constant and known. The algorithm is based on the fact that the earliest reflected signals obtained from a particular voxel depend either linearly or quadratically on the absorption coefficient in that voxel. By solving the discrete model in the forward direction in a region where the absorption coefficient has been calculated already, the absorption coefficients in the voxels on the boundary of the region can be calculated using interpolation. Results show that simple absorptive regions can be accurately recovered