  We present a generalized version of the Path Interchange Zel'dovich
Approximation (PIZA; Croft and Gaztanaga 1997; hereafter CG97), which may be
used to reconstruct density and velocity fields from realistic galaxy redshift
surveys. The original PIZA does not include the possibility of using galaxies
in redshift space with a selection function. We map galaxy positions from
redshift to real space and from the Local Group rest frame to the CMB rest
frame. To take account of the selection function, we minimize the mass-weighted
action. We apply our new method to mock galaxy catalogues and find it offers an
improvement in reconstructions over linear theory. Applying PIZA to the PSCz we
can obtain real space density, initial density, and peculiar velocity fields,
bulk velocities and the dipole. Comparison of our reconstructed dipole with the
CMB dipole gives beta=0.6
