  In this work we introduce a new Radon transform which arises from a new
modality of Compton Scattering Tomography (CST). This new system is made of a
single detector rotating around a fixed source. Unlike some previous CST, no
collimator is used at the detector. Such a system allows us to collect
scattered photons coming from two opposite sides of the source-detector
segment, hence the manifold of the associated Radon transform is a family of
double circular arcs. As first main theoretical result, an analytic inversion
formula is established for this new Radon transform. This is achieved through
the formulation of the transform in terms of circular harmonic expansion
satisfying the consistency conditions in Cormack's sense. Moreover, a fast and
efficient numerical implementation via an alternative formulation based on
Hilbert transform is carried out. Simulation results illustrate the theoretical
feasibility of the new system. From a practical point of view, an uncollimated
detector system considerably increases the amount of collected data, which is
particularly significant in a scatter imaging system.
