Rebinning of conical projection data in compton imaging

This paper presents a rebinning method for the reconstruction from Compton scattered conical projection data. Our rebinning method converts the 3-D conical projection data set into a stack of 2-D parallel projection data set so that a variety of existing 2-D analytical reconstruction methods developed for conventional emission tomography can be directly used for Compton imaging. In our rebinning method, the following three steps are performed. (i) A cone surface is sampled with a serial of lines that pass through the apex of the cone. (ii) By using the rotating imaginary planes, which are perpendicular to the transaxial (x-y) plane and parallel to the z axis, the sampled projection lines, which are mostly perpendicular to the imaginary planes, are sorted at each rotation angle. (iii) The sorted lines, most of which are oblique in the transaxial plane, are approximated to equivalent 2-D parallel projections in the transaxial plane using the Fourier rebinning (FORE) technique. Since our method is very fast, it can be useful for rapidly reconstructing Compton scattered data using fast analytical reconstruction methods.