Computer simulation of the analytical reconstruction of electronically collimated single photon images

A Fourier-Hilbert transform method for reconstructing dual detector plane, electronically collimated, single photon images has been devised and computer simulations have been performed to test the efficacy of the method. Computer generated source distributions were used to produce two dimensional projection images assuming Compton scattering in the first detector plane and photoelectric absorption in the second. The projection images were presented as input data to the reconstruction process which reproduced the original source distribution as a series of tomographic slices. The resulting images were compared to the original source distribution. Simple line source distributions were reconstructed accurately. Point and arbitrary source distribution reconstructions suffered from artifacts due to the limited size of the detector planes. These results confirm that an analytical reconstruction process is possible for single photon electronic collimation and support the theoretical argument that cylindrical detector surfaces or rotating detector planes will be best suited for future tomographic implementation