  The estimation of the K\"all\'en-Lehmann spectral density from gauge
invariant lattice QCD two point correlation functions is proposed, and explored
via an inversion strategy based on Tikhonov regularisation. We test the method
on a mesonic toy model, showing that our methodology is competitive with the
traditional Maximum Entropy Method. As proof of concept the SU(2) glueball
spectrum for the quantum numbers $J^{PC}=0^{++}$ is investigated, for various
values of the lattice spacing, using the published data of arXiv:1910.07756.
Our estimates for the ground state mass are in good agreement with the
traditional approach, which is based on the large time exponential behaviour of
the correlation functions. Furthermore, the spectral density also contains
hints of excites states in the spectrum. Spectroscopic analysis of glueball
two-point functions therefore provides a straightforward and insightful
alternative to the traditional method based on the large time exponential
behaviour of the correlation functions.
