Positron emission tomography (PET) is a powerful metabolic imaging modality, which is designed to detect two anti-parallel 511 keV photons origniating from a positron-electron annihilation. However, it is possible that one or both of the annihilation photons undergo a Compton scattering in the object. This is more serious for a scanner operated in 3D mode or with large patients, where the scatter fraction can be as high as 40-60%. When one or both photons are scattered, the line of response (LOR) defined by connecting the two relevant detectors no longer passes through the annihilation position. Thus, scattered coincidences degrade image contrast and compromise quantitative accuracy. Various scatter correction methods have been proposed but most of them are based on estimating and subtracting the scatter from the measured data or incorporating it into an iterative reconstruction algorithm. By accurately measuring the scattered photon energy and taking advantage of the kinematics of Compton scattering, two circular arcs (TCA) in 2D can be identified, which describe the locus of all the possible scattering positions and encompass the point of annihilation. In the limiting case where the scattering angle approaches zero, the TCA approach the LOR for true coincidences. Based on this knowledge, a Generalized Scatter (GS) reconstruction algorithm has been developed in this thesis, which can use both true and scattered coincidences to extract the activity distribution in a consistent way. The annihilation position within the TCA can be further confined by adding a patient outline as a constraint into the GS algorithm. An attenuation correction method for the scattered coincidences was also developed in order to remove the imaging artifacts. A geometrical model that characterizes the different probabilities of the annihilation positions within the TCA was also proposed. This can speed up image convergence and improve reconstructed image quality. Finally, the GS algorithm has been adapted to deal with non-ideal energy resolutions. In summary, an algorithm that implicitly incorporates scattered coincidences into the image reconstruction has been developed. Our results demonstrate that this eliminates the need for scatter correction and can improve system sensitivity and image quality. / February 2016