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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.

The determination of quantitative estimates of activity such as the maximum and total counts in a volume are influenced by the partial volume effect. The magnitude of this effect varies with the nonstationary spatial resolution inherent in SPECT imaging, the size and shape of the object, and the relative concentration of the object to its background. The objective of this investigation was to determine if frequency distance relationship (FDR) restoration filtering can reduce the impact of distance-dependent spatial resolution on the quantitation of activity. An analytical projector was used to incorporate attenuation and distance-dependent blurring when simulating a set of small hot spherical objects in a cylindrical attenuator. Reconstruction was performed by filtered backprojection (FBP) with Bellini's method of attenuation correction. The simulations were filtered by: 1) three-dimensional (3-D) Butterworth filtering; 2) stationary parametric Wiener filtering; and 3) FDR restoration filtering regularized using Gaussian and parametric Wiener filters. The criteria used to compare the accuracy of quantitation were the center count ratios (CCR's) and total count ratios (TCR's). Both were determined as the ratio of observed counts over true counts. Results showed that after FDR restoration the TCR's varied less with location, and for both CCR's and TCR's the bias decreased compared to Butterworth filtering.

A non-iterative SPECT reconstruction method is presented which consists of pre-processing the projection data for compensation of scatter, attenuation and the detector response prior to ramp filtered backprojection. Scatter is compensated for using the dual-photopeak window (DPW) method, attenuation is compensated for using Bellini's method, and compensation for the nonstationary detector response and noise suppression is performed with a frequency distance principle (FDP) Wiener filter. This approach was compared to a number of different processing methods using a Monte Carlo simulation study of an anthropomorphic digitized phantom of the liver and spleen. The DPW/FDP Wiener filtering method was shown to provide accurate quantitation of the liver as well as an increase in the ratio of tumor contrast to background noise as compared to Butterworth smoothing.