Analytical considerations of photon attenuation and system response function in SPECT reconstruction

Abstract

A unified framework for image reconstruction in single-photon emission computed tomography (SPECT) is proposed for modeling of the effects of photon attenuation and of the imaging-system point-spread function (PSF). This framework provides a basis for analysis of the mathematical properties of the SPECT reconstruction problem. We introduce an average-attenuation factor that is calculated along each projection line. Under certain conditions, a one-step correction method employing this average-attenuation factor compensates completely for the effects of both photon attenuation and PSF. In addition, a new hybrid approach is proposed that uses the one-step correction method at the initial step and shifts to a modified iterative Chang’s method in the subsequent iterations. We implemented both the iterative Chang’s method and our hybrid method in computer simulation studies. The results demonstrate that (a) our onestep correction method significantly improves the quality of reconstructed images over those with Chang’s one-step method; (b) our hybrid approach converges faster than does the iterative Chang’s method and produces reconstructed images of high quality.