Out-of-plane photon compensation for 3-D SPECT image reconstruction with generalized matrix inverses

A computationally efficient 3-D image reconstruction method which compensates for detected out-of-plane photons has been developed for SPECT image reconstruction with generalized matrix inverses (GMI). Fully 3-D image reconstruction is approximated by a series of coupled 2-D image reconstructions for projection data acquired with parallel hole collimators, significantly reducing computer memory requirements for GMI reconstruction. In this method, projection data are compensated for detected scattered photons using dual energy window scatter subtraction (Step 1). An initial source activity estimate in each transverse plane is then made, with 3-D detector response modeled in the system matrix (Step 2). Using these activity estimates, the contributions of out-of-plane unscattered photons are modeled and subtracted from the projection data, and an updated source activity estimate is computed (Step 3). This reconstruction method was evaluated using projection data from a Monte Carlo simulated myocardial perfusion study. Lesion contrast in the myocardium increases from 69% to 83% and activity spillover from the myocardium into the adjacent cardiac blood pool is reduced by 47% for noise-free projection data. For projection data with simulated Poisson noise, activity estimates from Step 3 are inferior to those from Step 2. Additional tests show that activity estimation is very sensitive to the source activity distribution used for out-of-plane unscattered photon compensation and thus the compensation technique of Step 3 may have only limited practical applications to count-limited SPECT studies