The development of radon transforms associated to compton scatter imaging concepts

For more than three decades, the exploitation of Compton scattering has led to significant progress in imaging the inner parts of an optically opaque object. In this imaging process, the Compton scattering angle plays an essential role as it labels the recorded data, suppressing the motion of the scanning camera, as well as generates new geometric manifolds on which radiation measurements are made and thereby introducing new relevant Radon transforms. The present paper is aimed to synthetize the conceptual development of Compton scattering imaging in order to gain a constructive overview and possibly induce a further innovative growth to it. We believe this may lay foundation to new mathematical tools as well as lead to a great diversity of applications.