Next-generation neutrinoless double beta decay experiments aim for half-life sensitivities of ~$10^{27}$ yr, requiring suppressing backgrounds to <1 count/tonne/yr. For this, any extra background rejection handle, beyond excellent energy resolution and the use of extremely radiopure materials, is of utmost importance. The NEXT experiment exploits differences in the spatial ionization patterns of double beta decay and single-electron events to discriminate signal from background. While the former display two Bragg peak dense ionization regions at the opposite ends of the track, the latter typically have only one such feature. Thus, comparing the energies at the track extremes provides an additional rejection tool. The unique combination of the topology-based background discrimination and excellent energy resolution (1% FWHM at the Q-value of the decay) is the distinguishing feature of NEXT. Previous studies demonstrated a topological background rejection factor of ~5 when reconstructing electron-positron pairs in the $^{208}$Tl 1.6 MeV double escape peak (with Compton events as background), recorded in the NEXT-White demonstrator at the Laboratorio Subterraneo de Canfranc, with 72% signal efficiency. This was recently improved through the use of a deep convolutional neural network to yield a background rejection factor of ~10 with 65% signal efficiency. Here, we present a new reconstruction method, based on the Richardson-Lucy deconvolution algorithm, which allows reversing the blurring induced by electron diffusion and electroluminescence light production in the NEXT TPC. The new method yields highly refined 3D images of reconstructed events, and, as a result, significantly improves the topological background discrimination. When applied to real-data 1.6 MeV $e^-e^+$ pairs, it leads to a background rejection factor of 27 at 57% signal efficiency.
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