  We present a new method, based on Gaussian process regression, for
reconstructing the continuous $x$-dependence of parton distribution functions
(PDFs) from quasi-PDFs computed using lattice QCD. We examine the origin of the
unphysical oscillations seen in current lattice calculations of quasi-PDFs and
develop a nonparametric fitting approach to take the required Fourier
transform. The method is tested on one ensemble of maximally twisted mass
fermions with two light quarks. We find that with our approach oscillations of
the quasi-PDF are drastically reduced. However, the final effect on the
light-cone PDFs is small. This finding suggests that the deviation seen between
current lattice QCD results and phenomenological determinations cannot be
attributed solely on the Fourier transform.
