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In this work we introduce a new Radon transform which arises from a newmodality of Compton Scattering Tomography (CST). This new system is made of asingle detector rotating around a fixed source. Unlike some previous CST, nocollimator is used at the detector. Such a system allows us to collectscattered photons coming from two opposite sides of the source-detectorsegment, hence the manifold of the associated Radon transform is a family ofdouble circular arcs. As first main theoretical result, an analytic inversionformula is established for this new Radon transform. This is achieved throughthe formulation of the transform in terms of circular harmonic expansionsatisfying the consistency conditions in Cormack's sense. Moreover, a fast andefficient numerical implementation via an alternative formulation based onHilbert transform is carried out. Simulation results illustrate the theoreticalfeasibility of the new system. From a practical point of view, an uncollimateddetector system considerably increases the amount of collected data, which isparticularly significant in a scatter imaging system.

Analytic inversion of a Radon transform on double circular arcs with applications in Compton Scattering Tomography