  We present a Bayesian reconstruction method which maps a galaxy distribution
from redshift-space to real-space inferring the distances of the individual
galaxies. The method is based on sampling density fields assuming a lognormal
prior with a likelihood given by the negative binomial distribution function
modelling stochastic bias. We assume a deterministic bias given by a power law
relating the dark matter density field to the expected halo or galaxy field.
Coherent redshift-space distortions are corrected in a Gibbs-sampling procedure
by moving the galaxies from redshift-space to real-space according to the
peculiar motions derived from the recovered density field using linear theory
with the option to include tidal field corrections from second order Lagrangian
perturbation theory. The virialised distortions are corrected by sampling
candidate real-space positions (being in the neighbourhood of the observations
along the line of sight), which are compatible with the bulk flow corrected
redshift-space position adding a random dispersion term in high density
collapsed regions. The latter are defined according to the eigenvalues of the
Hessian. This approach presents an alternative method to estimate the distances
to galaxies using the three dimensional spatial information, and assuming
isotropy. Hence the number of applications is very broad. In this work we show
the potential of this method to constrain the growth rate up to $k$ ~ 0.3 $h$
Mpc$^{-1}$. Furthermore it could be useful to correct for photo-metric redshift
errors, and to obtain improved BAO reconstructions.
