Tomography from Scattered Signals Obeying the Stationary Radiative Transport Equation

We study computerized tomography from scattered signals based on the stationary radiative transport equation which is a mathematical model of particle propagation with absorption and scattering by media. Discontinuity of the solution induced by a proper boundary condition plays an essential role. The jump in the discontinuities leads the X-ray transform of the attenuation coefficient, and thus X-ray inversion algorithms enable us to reconstruct it. Numerical experiments in two dimensions are exhibited to support its feasibility in quantitative reconstruction.