Reconstruction methods and completeness conditions for two Compton data models

Two different models are proposed for the data produced in a Compton imaging device. A sequence of equations, which relate the model to the distribution of radioactivity that is being imaged, is developed for each of the two models. No series expansions are used in these developments. On the basis of these sequences of equations, a completeness condition is developed for each of the two models. These completeness conditions may prove useful in the future in determining appropriate shapes, configurations, and motions of the device's detectors. A computer simulation is performed to verify one of these sequences of equations. A computer simulation is also performed to demonstrate that this sequence of equations can produce more accurate images than a backprojection reconstruction method. In addition, a procedure is proposed that could mitigate the effects of the Mein-Nishina distribution, the Doppler broadening, and the variability in the data due to the random generation of photons. (C) 2005 Optical Society of America.