Fast spatial-domain convolution which accounts for system spatial resolution

The modeling of the distance-dependent spatial resolution of SPECT imaging in the projector and backprojector pair used in iterative reconstruction improves the resulting slices both quantitatively and qualitatively. By using small, spatial-domain, convolution masks to model the blurring from one image plane to the next, Gaussian diffusion can markedly reduce the computational burden. The problem with Gaussian diffusion is that aliasing distorts the coefficients of the masks such that there can be a significant loss in the accuracy with which resolution is modeled. The use of integration of the probability density function of the Gaussian function over pixel boundaries as opposed to delta-function sampling, an effective value for the standard deviation of the Gaussian used in blurring from one plane to the next, and diffusion over multiple plane steps were investigated as possible methods to diminish the impact of aliasing on accuracy. For large pixel sizes the combined use of all three methods was determined to be needed to reduce the impact of aliasing on accuracy. As the pixel size decreases, the use of any of the methods results in a significant improvement in accuracy, with an 8 plane diffusion step resulting in an almost ideal response.