Imaging processes built on the Compton scattering effect have been under continuing investigation since it was first suggested\r\nin the 50s. However, despite many innovative contributions, there are still formidable theoretical and technical challenges to\r\novercome. In this paper, we review the state-of-the-art principles of the so-called scattered radiation emission imaging. Basically,\r\nit consists of using the cleverly collected scattered radiation from a radiating object to reconstruct its inner structure. Image\r\nformation is based on the mathematical concept of compounded conical projection. It entails a Radon transform defined on\r\ncircular cone surfaces in order to express the scattered radiation flux density on a detecting pixel. We discuss in particular\r\ninvertible cases of such conical Radon transforms which form a mathematical basis for image reconstruction methods. Numerical\r\nsimulations performed in two and three space dimensions speak in favor of the viability of this imaging principle and its potential\r\napplications in various fields.
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