Cormack-type inversion of attenuated Radon transform

The reconstruction of a function from its attenuated Radon transform (AtRT) finds many applications in medical and physical imaging. A lot of different algorithms of inversion of AtRT have been described based on the Novikov formula. In this paper, we consider a particular case of the AtRT, when the attenuation is axially symmetric. The reconstruction algorithm is based on circular harmonic decomposition. The work is in fact a natural generalization of the Cormack algorithm for the exponential Radon transform. This method of reconstruction is applicable to axially symmetric attenuated Radon transform with a complex attenuation and can be used for reconstruction in polarized tomography of stress tensor fields.