The mathematics of computerized tomography
The mathematics of computerized tomography
Incorporation of Anatomical MR Data for Improved Dunctional Imaging with PET
IPMI '91 Proceedings of the 12th International Conference on Information Processing in Medical Imaging
Penalized maximum-likelihood image reconstruction using space-alternating generalized EM algorithms
IEEE Transactions on Image Processing
| Hi-index | 0.00 |
The popular Radon transform approximation used in the modeling and reconstruction of positron emission tomography (PET) images fails to account for the non-trivial size of PET detectors. Currently, all reconstruction algorithms which account for detector width are based on the iterative EMML (expectation maximization maximum likelihood) method which uses computational approximations of the true point spread function. Starting with the angle-of-view model for the point spread function, a new integral equation model is obtained by applying a simple linear transformation to the emission sinogram which produces detections in arcs of various widths, instead of the usual detector tubes. In this paper, an exact mathematical representation for the new point spread function is obtained in terms of line integrals involving the Green's function and Poisson kernel for the unit disk. By applying appropriate mathematical transforms, this representation leads to a method for reconstructing two dimensional PET images in terms of an orthogonal basis consisting of tensor products of classical harmonics and Bessel functions. The paper contains details of the mathematical derivation of the representation for the point spread function, and the resulting reconstruction technique. It also contains numerical results which indicate that this new method produces images which are comparable (and sometimes superior) in quality to the EMML method, with a reconstruction speed which is similar that of the filtered back projection method.