  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 Subterr\'aneo 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.
