  We present a novel approach for the reconstruction of spectra from Euclidean
correlator data that makes close contact to modern Bayesian concepts. It is
based upon an axiomatically justified dimensionless prior distribution, which
in the case of constant prior function $m(\omega)$ only imprints smoothness on
the reconstructed spectrum. In addition we are able to analytically integrate
out the only relevant overall hyper-parameter $\alpha$ in the prior, removing
the necessity for Gaussian approximations found e.g. in the Maximum Entropy
Method. Using a quasi-Newton minimizer and high-precision arithmetic, we are
then able to find the unique global extremum of $P[\rho|D]$ in the full
$N_\omega\gg N_\tau$ dimensional search space. The method actually yields
gradually improving reconstruction results if the quality of the supplied input
data increases, without introducing artificial peak structures, often
encountered in the MEM. To support these statements we present mock data
analyses for the case of zero width delta peaks and more realistic scenarios,
based on the perturbative Euclidean Wilson Loop as well as the Wilson Line
correlator in Coulomb gauge.
