We are developing novel insert devices for existing whole body PET scanners to achieve better resolution in selected regions of interest such as the head, neck, breast or abdomen. The insert considered here is a full ring of high resolution detectors, which can be placed around the object of interest. Adding the insert inside the scanner leads to three different types of coincidences: insert-insert, insert-scanner and scanner-scanner. The insert-insert and scanner-scanner coincidences are similar to the coincidences obtained in a traditional PET system. The insert-scanner coincidences have an inherent fan-beam geometry for which a spatially variant system matrix is proposed. The system matrix is computed using the intersection of a fan beam with a pixel. A filtered back-projection (FBP) algorithm for the insert-scanner geometry is presented. This FBP algorithm yields images with significantly reduced artifacts compared to FBP reconstructions on insert-scanner data rebinned into parallel beams. This is demonstrated using simulated point source data acquired using SimSET. It is proposed to use a penalized ML-EM (PML-EM) algorithm using a log-cosh roughness penalty function to reconstruct a single activity distribution from all three data sets. This is demonstrated qualitatively using simulated point source data. A quantitative comparison of PML-EM and FBP was performed on data acquired from insert-scanner coincidences using a phantom with hot and cold tumors imaged in an experimental setup. The quantitative studies demonstrate that the resolution/noise tradeoff of PML-EM is improved relative to FBP.