Linear and iterative reconstruction algorithms for a novel PET-insert scanner

Tai, et al. are developing insert devices for existing clinical PET scanners to improve the image resolution. Adding the insert inside the scanner leads to three types of coincidences: insert-insert, insert-scanner and scanner-scanner. The challenges in image reconstruction include development of a linear reconstruction algorithm for the insert-scanner coincidences, development of a linear reconstruction algorithm that incorporates all measurements, and development of an iterative (expectation-maximization) algorithm to form a maximum likelihood estimate of the image given all of the data. The data from the set of insert-insert coincidences and from the set of scanner-scanner coincidences each can be used in conventional linear reconstruction algorithms based on data from a ring of detectors. However, the geometry of an insert ring and a scanner ring together is analogous to the fan-beam geometry of fourth generation transmission tomography systems; this analogy leads to a new linear reconstruction algorithm for these data. The resulting algorithm was implemented on both simulated and experimental data, yielding promising results with few artifacts. Our development of an iterative algorithm is based on the standard expectation-maximization algorithm. The novelty of the iterative algorithm is in the incorporation of the details of the geometry, which is based in part on our characterization of the insert-scanner geometry.