Simultaneously constraining SPECT activity estimates with primary and secondary energy window projection data

Single photon emission computed tomography (SPECT) projection data acquired in primary (photopeak) and secondary energy windows provide independent constraints on the source activity distribution. These constraints are used simultaneously and a single matrix equation is solved to estimate source activity. This simultaneous constraint reconstruction method (I) is evaluated in a Monte Carlo experiment and compared with activity estimation using only primary energy window projection data with (m) and without (II) modeling the detection of scattered photons in the system matrix, and with dual energy window scatter subtraction (TV). The transport and detection of photons emitted by Tc-99m within a water-filled cylinder is simulated. Images are reconstructed using generalized matrix inverses, which are designed so that the estimated variance of the reconstructed source voxel activities is approximately constant. For 40 projection data sets with about one million counts/slice in the primary energy window, the mean activity in regions of interest is within 2.2%, 28.2%, 2.2% and 3.5% of the source model activity for reconstruction methods I-IV, respectively. The full-widths at half-maximum (FWHM) of resolution kernels from methods I and III differ on average by less than 1%; the FWHM of kernels from methods II and IV average 8% larger. In this experiment, the simultaneous constraint method yields no appreciable improvement in quantitative accuracy or resolution over the use of primary energy window data alone when the detection of scattered photons is modeled. These two methods are only slightly superior to activity estimation using dual energy window scatter subtraction