Reprojection and backprojection in SPECT image reconstruction

An algorithm compensating the deterministic effects of photon attenuation, scattering, and collimator divergence associated with quantitative SPECT (single-photon-emission computed tomography) images is presented. The compensation algorithm is based on a technique which traces the geometrical relations of pixels and projection rays. If the attenuation map of the source distribution and the collimator divergence function are known, the compensation is accurate. The implementation of the compensation algorithm within the reprojection processes is carried out in an iterative manner for computer-generated ideal data. Improvement in image reconstruction of SPECT is demonstrated. An analytical study of implementing the compensation algorithm the backprojection process is given. A Bayesian analysis is used to suppress the artifacts due to the low count detection of photons associated with SPECT. A comparison of the BIP (Bayesian image processing) and ML (maximum-likelihood) methods on image reconstruction is carried out for computer-generated ideal and Poisson randomized data. Improved images using the BIP method are obtained.