Estimating effective model kernel widths for PSF reconstruction in PET

Point-spread function (PSF) reconstruction algorithms include a kernel describing the spatial distribution of a point source's detection probability. While PSF reconstruction often helps to improve the spatial resolution and signal-to-noise ratio of these iterative algorithms, in some cases it can also lead to effects such as hyper-resolution, edge-overshoot, and degraded resolving power. We believe such artifacts could be caused in part by a mismatch between how the physical PSF is measured and how it is employed in reconstruction. In essence, the contribution of the numerical component of the point spread due to the discretization of the image and projection operators is usually neglected. If it were accounted for, the effective model kernel width used for PSF reconstruction should be smaller than the physical kernel width by an amount comparable to the numerical point spread in order to give an accurate prediction of the total physical point spread in the data. We have developed an image-based technique for estimating the appropriate effective width by adjusting it to achieve the correct diameter of small but finite hot spots in reconstructed images, as a function of radial offset. We have implemented this technique on an integrated MR/PET system by imaging arrays of positron beams in air. We find that for our system the effective model kernel width necessary to give accurate reconstruction is 27% smaller than the full physical width near the center of the FOV. Results for positron beam imaging, arrays of conventional point sources, image quality phantoms, and clinical human imaging are shown. The issues of convergence and contrast vs. noise performance are also addressed.