Correction for Shift-variant Characteristics of Single Photon Emission Computed Tomography Acquisition System Using Sensitivity Functions

The single photon emission computed tomography (SPECT) imaging system has shift-variant characteristics due to non-uniform attenuation of gamma-ray, collimator design, scattered photons, etc. In order to provide quantitatively accurate SPECT images, these characteristics should be compensated in the reconstruction. This paper presents a new method to correct the shift-variant characteristics, which is based on a continuous-discrete mapping model and filtered backprojection (FBP) method, in which the projection data are assumed to be acquired by narrow ray sum beams in the FBP method and the assumed data set is expressed as a linear combination of the actual projection data. Narrow ray sum beams are approximated by a weighted sum of the original sensitivity functions. Thus, at the reconstruction the projection data are first modified using an approximation and the FBP method is then applied to the corrected projection data and a SPECT image is reconstructed. We further propose a technique that requires the inversion of smaller matrices than the conventional algebraic method; the amount of calculation and memory space become smaller and the stability of the calculation is greatly improved as well. The results of the numerical simulations are also demonstrated.