I present a new quasi-linear method for reconstructing cosmological density and velocity
fields from all-sky redshift surveys. The method is used to reconstruct the velocity field,
dipole, bulk flows and distortion parameter (ß = Ω⁰.⁶/b from the PSCz survey.Analytic expressions for the cosmic variance and shot noise uncertainties on the reconstructed velocity field are presented. It is found that the uncertainties are reduced if
reconstruction is carried out in the Local Group frame. The uncertainty on the dipole
is also found.A generalized version of the Path Interchange Zel'dovich Approximation (PIZA ) is
presented. PIZA is a simple Lagrangian reconstruction method based on the Zel’dovich
Approximation and the Least Action Principle, which reconstructs cosmological fields
given the present day real space positions of galaxies. The generalizations take account
of redshift space distortions, incomplete sky coverage, and the selection function. The
method can be used to estimate ß from radial velocities, bulk flows and the dipole.Generalized PIZA has been tested using a set of PSCz-like simulations. The reconstructed radial peculiar velocity field is com pared with that o f the simulation and that
reconstructed by linear theory.The generalized PIZA is applied to the IRAS PSCz Survey. The dipole, bulk velocities and peculiar velocity field, and the derived value of ß are presented. The Local
Group is found to have an average displacement of 1225kms⁻¹ in the direction of
(l,b) = (264°,42°). From this it is found that (ß = 0.512 ± 0.141
