3D Compton scattering imaging with multiple scattering: analysis by FIO and contour reconstruction

3D Compton scattering imaging (CSI) is an upcoming concept exploiting the scattering of photons induced by the electronic structure of the object under study. The so-called Compton scattering rules the collision of particles with electrons and describes their energy loss after scattering. Although physically relevant, multiple-order scattering was so far not considered and therefore, only first-order scattering is generally assumed in the literature. The purpose of this work is to argument why and how a contour reconstruction of the electron density map from scattered measurement composed of first- and second-order scattering is possible (scattering of higher orders are here neglected). After the development of integral representations for the first- and second-order scattering, we approximate these models by Fourier integral operators (FIO) and study their smoothness properties. The second-order scattered radiation reveals itself to be structurally smoother than the radiation of first-order indicating that the contours of the electron density are essentially encoded within the first-order part. This opens the way to contour-based reconstruction techniques when considering multiple scattered data. Our main results, modeling and reconstruction scheme, are successfully implemented on synthetic and Monte-Carlo data. (paper)