An efficient three-dimensional unified projector-backprojector for SPECT reconstruction

A unified projector-backprojector (PBJ) which can easily be adapted for hardware implementation was tested in software for simultaneous compensation of attenuation, scatter, and detector response. The PBJ discretely models the system transform of isotopes distributed within attenuating media as line integrals and convolutions of discrete voxels, obtained using the sampling technique of averaging the photon emission or attenuation distribution over small cubic regions. Each line integral through the voxels is computed by recursion from the entry point of the projection ray intersecting with the voxel array to the exit point. During the recursive tracing, the attenuation factor is obtained, for each voxel, by halving the attenuating length of that voxel and adding to the previously accumulated attenuating length along that projection ray. The detector response and scatter are modeled as a convolution of the voxels with a Gaussian kernel whose shape is a function of distance from the detector, after subtraction of dual-energy-window data. Projecting a chest phantom of 128*128*64 to a 128*64*120 projection array took approximately 1 h on the Stellar computer. The PBJ was implemented into iterative maximum likelihood, maximum a posteriori probability, and filtered backprojection reconstructions. High-quality images were obtained using experimentally acquired projections.<>