On geometric aspects of circular arcs radon transforms for compton scatter tomography

If the classical line Radon transform (CLRT) has been a successful mathematical model for conventional radiation imaging modalities such as Computed Tomography (CT), Single Photon Emission Computed Tomography (SPECT) and Positron Emission Tomography (PET), the circular arc Radon transform (CART) is a potential mathematical model contender for Compton Scatter Tomography (CST). In this work we show that there are actually five classes of circular arcs on which Radon transforms can be defined and used as basis for five distinct CST modalities. These circular arcs are cut out from circles characterized by a fixed value of the power of the coordinate system origin. We also show how the five CART can be mapped onto respective CLRT, so that inversion formulas as well as some properties for function reconstruction, which are essential for working CST can be fully established.