This feasibility study is needed to determine how common it is for a diagnosis of recurrent cancer to be unclear even after standard diagnostic imaging tests have been completed. If the enrollment goal is reached (~60 patients enrolled in 18 months), a larger clinical trial is being planned to determine if PET/CT is helpful in making the diagnosis of recurrent cancer in situations where standard imaging tests have not been helpful. It is also expected that the results of this feasibility study will help to define exactly which patients should be enrolled in this larger clinical trial of PET/CT.