Many image-reconstruction methods have been proposed to improve the spatial resolution of positron emission tomography (PET) images and, thus, to produce better quantification. However, these techniques, which are designed for static images, may be inadequate for good reconstruction from dynamic data. We present a simple, but effective, reconstruction approach intended specifically for dynamic studies. First, the level of noise in dynamic PET data is reduced by smoothing along the time axis using a low-order approximation. Next, the denoised sinograms are restored spatially by the method of projections onto convex sets. Finally, images are reconstructed from the restored sinograms by ordinary filtered backprojection. We present experimental results that demonstrate substantial improvements in region-of-interest quantification in actual and simulated dopamine D-2 neuroreceptor-imaging studies of a monkey brain.