In this paper, we address the problem of denoising reconstructed small animal positron emission tomography (PET) images, based on a multiresolution approach which can be implemented with any transform such as contourlet, shearlet, curvelet, and wavelet. The PET images are analyzed and processed in the transform domain by modeling each subband as a set of different regions separated by boundaries. Homogeneous and heterogeneous regions are considered. Each region is independently processed using different filters: a linear estimator for homogeneous regions and a surface polynomial estimator for the heterogeneous region. The boundaries between the different regions are estimated using a modified edge focusing filter. The proposed approach was validated by a series of experiments. Our method achieved an overall reduction of up to 26% in the %STD of the reconstructed image of a small animal NEMA phantom. Additionally, a test on a simulated lesion showed that our method yields better contrast preservation than other state-of-the art techniques used for noise reduction. Thus, the proposed method provides a significant reduction of noise while at the same time preserving contrast and important structures such as lesions.