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Positron emission tomography (PET) images suffer from low spatial resolution. To improve the spatial resolution, we previously proposed a sinogram-based super-resolution (SR) algorithm for a whole-body PET scanner, by assuming space invariant blur. However, since the spatial resolution of a sinogram varies along the radial direction due to parallax error, this algorithm is not appropriate for providing a high-resolution sinogram with reduction of parallax error. In this paper, we propose a novel and efficient sinogram-based SR algorithm that is suitable even for a small animal PET scanner by using space variant blur matrices. In the algorithm, we estimate the space variant blur matrices through a Monte Carlo simulation and use them for the SR process to obtain a high-resolution sinogram. Using a Derenzo phantom and a line source, we demonstrate in a real PET scanner, microPET R4, that the proposed SR algorithm noticeably improves the spatial resolution while alleviating its space variance. By applying the proposed SR algorithm, the full width at half-maximum (FWHM) value reaches 1.2 mm at the system center and 1.63 mm with a considerable parallax error reduction at a radial position of 4 cm.