  The standard approach to compute the glueball spectrum on the lattice relies
on the evaluation of effective masses from two-point correlation functions of
operators with the quantum numbers of the desired state. In this work, we
propose an alternative procedure, based on the numerical computation of smeared
spectral densities. Even though the extraction of the latter from lattice
correlators is a notoriously ill-posed inverse problem, we show that a recently
developed numerical method, based on the Backus-Gilbert regularization,
provides a robust way to evaluate a smeared version of the spectral densities.
Fitting the latter to a combination of Gaussians, we extract the masses of the
lightest glueball and of its first excitation in the spectrum of the theory.
While the preliminary results presented in this contribution are restricted to
simulations at finite lattice spacing and finite volume, and for the purely
gluonic sector of QCD, they represent the first step in a systematic
investigation of glueballs using spectral-reconstruction methods.
