  The computation of the parton distribution functions (PDF) or distribution
amplitudes (DA) of hadrons from first principles lattice QCD constitutes a
central open problem. In this study, we present and evaluate the efficiency of
a selection of methods for inverse problems to reconstruct the full
$x$-dependence of PDFs. Our starting point are the so called Ioffe time PDFs,
which are accessible from Euclidean time calculations in conjunction with a
matching procedure. Using realistic mock data tests, we find that the ill-posed
incomplete Fourier transform underlying the reconstruction requires careful
regularization, for which both the Bayesian approach as well as neural networks
are efficient and flexible choices.
