The search for neutrinoless double beta decay is the most promising approach to determine whether the neutrino is its own antiparticle. If detected, it will be a first demonstration of lepton number violation, with far-reaching implications in particle physics and cosmology. Because of the extremely long half-lives of the decay (>10^26 years), a successful detection requires outstanding background suppression capability. The NEXT experiment searches for neutrinoless double beta decay in xenon-136, using a high-pressure gaseous xenon time projection chamber. While other experiments in the field rely predominantly on a high energy resolution for discriminating between candidate signal and background events, NEXT has in addition a unique capability to reconstruct the full topology of events in 3D and thus provide an extra handle for signal-background discrimination. In this talk we will present a new image reconstruction method recently developed at Ben-Gurion University, which allows for unprecedented accuracy in track reconstruction, resulting in a 4-5 fold improvement in background suppression. We will demonstrate the use of this method on real data from the experiment, showing – for the first time – sharp images of two-neutrino double beta decay candidate tracks.