Summary: The standard model for positron emission tomography is a First Kind Fredholm integral equation relating the emission means to the detection means in which the kernel is the probability that an annihilation at a point in image space is detected in a detector tube. This paper contains an overview of recent results on the precise mathematical representation of this kernel and resulting reconstruction algorithms by orthogonal series methods. These algorithms are compared with the standard filtered backprojection (FBP) and expectation maximization maximum likelihood (EMML) algorithms for reconstructing a discontinuous cardiac phantom. The simulations indicate that at least one of the new orthogonal series algorithms produces images with resolution superior to the FBP images, in about \(2\%\) of the time required to compute the EMML reconstruction.
For the entire collection see [Zbl 1003.00013].