  We present a new algorithm to reconstruct the Galactic free electron density
from pulsar dispersion measures. The algorithm performs a nonparametric
tomography for a density field with an arbitrary amount of degrees of freedom.
It is based on approximating the Galactic free electron density as the product
of a profile function with a statistically isotropic and homogeneous log-normal
field. Under this approximation the algorithm generates a map of the free
electron density as well as an uncertainty estimate without the need of
information about the power spectrum. The uncertainties of the pulsar distances
are treated consistently by an iterative procedure. We test the algorithm using
the NE2001 model with modified fluctuations as a Galaxy model, pulsar
populations generated from the Lorimer population model, and mock observations
emulating the upcoming Square Kilometer Array. We show the quality of the
reconstruction for mock data sets containing between 1000 and 10000 pulsars
with distance uncertainties up to 25%. Our results show, that with the SKA
nonparametric tomography of the Galactic free electron density becomes
feasible, but the quality of the reconstruction is very sensitive to the
distance uncertainties.
