The possibility of complete restoration of variable collimator response in SPECT imaging

Spatial resolution of SPECT imaging is mainly limited by the geometry of collimator holes. A long collimator hole with a small diameter improves the spatial resolution at the cost of low detection efficiency. With a finite size for the holes, the resolution changes as a function of the distance from the collimator surface. Lewitt et al. (1988) developed an approximate restoration algorithm to correct for the distance-dependent collimator blurring by the Fourier transform of sinogram. Van Elmbt et al. (1993) presented an analytical formula assuming an approximated resolution variation function. In this work, an accurate restoration procedure is investigated for a fan integral projection data based on the collimator hole geometry. The variable collimator response is illustrated as a fan-region integral of the radionuclide distribution, which is different from the conventional line integral, when using the FBP algorithm to reconstruct the image. In a parallel-beam acquisition geometry, if the radionuclide distribution is restricted to a bounded region, the line integral can be accurately computed from the fan integral near the boundary, then by a bootstrap technique, all these line integrals can be obtained. Therefore the variable collimator response can be completely restored theoretically.