An analytical image reconstruction algorithm to compensate for scattering angle broadening in Compton cameras

Compton cameras have been developed for use in gamma-ray astronomy and nuclear medicine. Their defining merit is that they do not need collimators; however, on the demerit side, they need inversion procedures for image reconstruction, since a measured datum is proportional to the integration of incident gamma rays along a cone surface with the same Compton scattering angle. First, an iteration method was adopted for this task. Later, analytical methods were found under restricted conditions. Parra (2000 IEEE Trans. Nucl. Sci. 47 1543-50) deduced a purely analytical reconstruction algorithm for a complete set of scattering-projection data that include data at all the scattering angles. Tomitani and Hirasawa (2002 Phys. Med. Biol. 47 2129-45) found that by making a slight modification, Parra's algorithm could be extended to the scattering-projection data in limited scattering angles. However, their algorithm neglected the effects of practical problems that cause the degradation of spatial resolution. Sources of degradation were identified as noise in the energy signal of their front detector and the Doppler effect in the scattering process. In this paper, we first analyse the effects of these sources on the angular resolution of the scattering-projection data and then present a revised reconstruction algorithm in which these two factors are incorporated. Simulation studies on digital phantoms reveal that the algorithm can reconstruct images even when these two factors are included.