Direct reconstruction methods for the Compton scattering camera for use in SPECT

A novel type of gamma-camera based on coincident detection of photons on two detecting planes, sometimes called electronic collimation, has been demonstrated elsewhere to have the potential to better the counting statistics and energy resolution of the Anger camera. As Compton scattering is used to localise photon direction vectors, the projections can be considered to be a set of integrals over the surfaces of cones. Thus the algorithms needed for fully three-dimensional reconstruction differ from those used in conventional tomography. If a complete set of projections is collected over an infinitely extending plane it is shown that the reconstruction problem is not only analytically solvable but also overspecified in the absence of measurement uncertainties. However, practical limitations dictate that all measurements are utilised. Relationships in Fourier space connecting a subset of the projections to the source image and to parallel-ray projections are developed. Results of computer simulations are presented which indicate the performance characteristics necessary in the detector to achieve usable reconstruction