  The goal of the NEXT experiment is the observation of neutrinoless double
beta decay in $^{136}$Xe using a gaseous xenon TPC with electroluminescent
amplification and specialized photodetector arrays for calorimetry and
tracking. The NEXT Collaboration is exploring a number of reconstruction
algorithms to exploit the full potential of the detector. This paper describes
one of them: the Maximum Likelihood Expectation Maximization (ML-EM) method, a
generic iterative algorithm to find maximum-likelihood estimates of parameters
that has been applied to solve many different types of complex inverse
problems. In particular, we discuss a bi-dimensional version of the method in
which the photosensor signals integrated over time are used to reconstruct a
transverse projection of the event. First results show that, when applied to
detector simulation data, the algorithm achieves nearly optimal energy
resolution (better than 0.5% FWHM at the Q value of $^{136}$Xe) for events
distributed over the full active volume of the TPC.
