Focused beamformers have been extensively used in phased-array signal processing, leading to simple and efficient imaging procedures, with high sensitivity and resolution. The beamshape acts as a spatial filter, scanning the intensity of the incoming signal for particular locations. We introduce beamforming in the context of Positron Emission Tomography (PET), and propose a new beamformer called Sinobeam. Inspired by the Flexibeam framework, we sample the beamforming weights from an analytically-specified beamforming function. Since the weights are data-independent, the resulting imaging algorithm is extremely efficient, while presenting better resolution and contrast than state of the art methods as demonstrated by simulation.