  In reconstruction analysis of galaxy redshift surveys, one works backwards
from the observed galaxy distribution to the primordial density field in the
same region, then evolves the primordial fluctuations forward in time with an
N-body code. This incorporates assumptions about the cosmological parameters,
the properties of primordial fluctuations, and the biasing relation between
galaxies and mass. These can be tested by comparing the reconstruction to the
observed galaxy distribution, and to peculiar velocity data. This paper
presents a hybrid reconstruction method that combines the `Gaussianization''
technique of Weinberg(1992) with the dynamical schemes of Nusser & Dekel(1992)
and Gramann(1993). We test the method on N-body simulations and on N-body mock
catalogs that mimic the depth and geometry of the Point Source Catalog Redshift
Survey and the Optical Redshift Survey. This method is more accurate than
Gaussianization or dynamical reconstruction alone. Matching the observed
morphology of clustering can limit the bias factor b, independent of Omega.
Matching the cluster velocity dispersions and z-space distortions of the
correlation function xi(s,mu) constrains the parameter beta=Omega^{0.6}/b.
Relative to linear or quasi-linear approximations, a fully non-linear
reconstruction makes more accurate predictions of xi(s,mu) for a given beta,
thus reducing the systematic biases of beta measurements and offering further
scope for breaking the degeneracy between Omega and b. It also circumvents the
cosmic variance noise that limits conventional analyses of xi(s,mu). It can
also improve the determination of Omega and b from joint analyses of redshift
  & peculiar velocity surveys as it predicts the fully non-linear peculiar
velocity distribution at each point in z-space.
