  Parton distribution functions (PDFs) are nonperturbative objects defined by
nonlocal light-cone correlations. They cannot be computed directly from Quantum
Chromodynamics (QCD). Using a standard lattice QCD approach, it is possible to
compute moments of PDFs, which are matrix elements of local operators.
Recently, an alternative approach has been proposed, based on the introduction
of quasi-parton distribution functions (quasi-PDFs), which are matrix elements
of equal-time spatial correlations and hence calculable on lattice. Quasi-PDFs
approach standard PDFs in the limit of very large longitudinal proton momenta
$P^z$. This limit is not attainable in lattice simulations, and quasi-PDFs fail
to reproduce PDFs at high fractional longitudinal momenta. In this paper, we
propose a method to improve the reconstruction of PDFs by combining information
from quasi-PDFs and from the Mellin moments of regular PDFs. We test our method
using the diquark spectator model for up and down valence distributions of both
unpolarized and helicity PDFs. In the future, the method can be used to produce
PDFs entirely based on lattice QCD results.
