  We consider the problem of "measuring" the K\"all\'en-Lehmann spectral
density of a particle (be it elementary or bound state) propagator by means of
4d lattice data. As the latter are obtained from operations at (Euclidean
momentum squared) p^2>=0, we are facing the generically ill-posed problem of
converting a limited data set over the positive real axis to an integral
representation, extending over the whole complex p^2-plane. We employ a linear
regularization strategy, commonly known as the Tikhonov method with Morozov
discrepancy principle, with suitable adaptations to realistic data, e.g. with
unknown threshold. An important virtue over the (standard) maximum entropy
method is the possibility to also probe unphysical spectral densities, as, for
example, of a confined gluon. We apply our proposal here to "physical" mock
spectral data as a litmus test and then to the lattice SU(3) Landau gauge gluon
at zero temperature.
