We propose a non-iterative method called Local Regression FBP (LR-FBP) for emission tomographic image reconstruction with resolution recovery. The method processes the sinogram volume data by running a two-dimensional local regression (LR) algorithm over the image projections - this has the effect of improving data signal-to-noise-ratios (SNR) as it fits the image projections thus reducing noise. Resolution recovery is then performed on the fit sinogram and the Filtered Back Projection (FBP) reconstruction using a ramp filter is then applied. The simulation studies presented show that LR-FBP gives lower bias and improved resolution compared to conventional FBP. Imaging studies using the IndyPET-Ell Small Animal PET scanner and the Siemens/CTI Biograph-16 PET/CT scanner show qualitative improvements in image resolution and contrast, as well as possible quantitative improvements in contrast recovery.