Improved SPECT quantitation using fully three-dimensional iterative spatially variant scatter response compensation

The quality and quantitative accuracy of iteratively reconstructed SPECT images improves when better point spread function (PSF) models of the gamma camera are used during reconstruction. In this paper, inclusion in the PSF model of photon crosstalk between different slices caused by limited gamma camera resolution and scatter is examined. A three-dimension (3-D) projector back-projector (proback) has been developed which models both the distance dependent detector point spread function and the object shape-dependent scatter point spread function of single photon emission computed tomography (SPECT). A table occupying only a few megabytes of memory is sufficient to represent this scatter model. The contents of this table are obtained by evaluating an analytical expression for object shape-dependent scatter. The proposed approach avoids the huge memory requirements of storing the full transition matrix needed for 3-D reconstruction including object shape-dependent scatter. In addition, the method avoids the need for lengthy Monte Carlo simulations to generate such a matrix. In order to assess the quantitative accuracy of the method, reconstructions of a water filled cylinder containing regions of different activity levels and of simulated 3-D brain projection data have been evaluated for technetium-99m. It is shown that fully 3-D reconstruction including complete detector response and object shape-dependent scatter modeling clearly outperforms simpler methods that lack a complete detector response and/or a complete scatter response model. Fully 3-D scatter correction yields the best quantitation of volumes of interest and the best contrast-to-noise curves