Speaker
Description
Reconstructing spectral information from Euclidean lattice correlators is a central inverse problem in lattice QCD. The correlator is related to the underlying spectrum through a Laplace-type transform, but inverting this relation from finite and noisy data is severely ill-conditioned. In this contribution, we discuss two complementary strategies for approaching this problem. The first attempts to recover spectral information by numerically inverting the Laplace relation itself. The second avoids a full inversion and instead extracts spectral information through a parametrized or smeared representation of the correlator, such as a finite set of exponential contributions or localized spectral structures. Using mock lattice-like correlators, including noisy data and near-degenerate spectral contributions, we compare the behavior of these strategies across several algorithmic workflows. The comparison illustrates the different roles of direct inversion, regularized reconstruction, and parametrized spectral extraction in lattice-QCD spectroscopy.