Modeling of the Point Spread Function by Numerical Calculations in Single-Pinhole and Multipinhole SPECT Reconstruction

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In conventional reconstruction of single photon emission computed tomography (SPECT) data acquired with a single-pinhole or multipinhole system, the point spread function (PSF) may be either approximated by some analytical equations or substituted by the sensitivity function, which is the integral of the PSF. We have developed a method to numerically calculate the PSF for a pinhole system in order to improve image resolution over a sensitivity-function-based method. The method calculates the probability of photon penetration through the pinhole edges using a ray-tracing approach. To calculate the transmission by the collimator plate along each ray, we trace the ray through the collimator by analytical calculations. The PSF is calculated for only one detector angle, and a Gaussian rotator is used to rotate the image grid for other detector angles in the iterative reconstruction. To evaluate our method, we measured the sensitivities of four keel-edged single-pinhole plates and scanned an ultramicro Derenzo phantom on a single-pinhole system and a five-pinhole system and performed two mouse bone scans on the five-pinhole system using the 140 keV photons of Tc-99m. The numerical calculations of sensitivities for the single-pinhole plates agreed well with the measurements. Results for both types of data scans showed that modeling of the PSF improved image resolution. In conclusion, we found that modeling of the PSF by numerical calculations increases the resolution of reconstruction for single-pinhole and multipinhole SPECT imaging.