Reconstruction Analysis - Part One - Redshift-Space Deprojection in the Quasi Nonlinear Regime

We present a new method for the extraction of the true three-dimensional velocity and density fields from the non-linear redshift-space projected density field. The method is based on the non-linear, non-local transformation of the density field. We assume a curl-free velocity field, although in the formulation presented here this assumption can be dropped. Toy models with special symmetry are used to test the intrinsic accuracy of the method compared with linear theory. Finding significant improvement, we then test the method in more detail on N-body simulations, considering the problems associated with sampling of the density field using sparse, magnitude-limited galaxy redshift surveys. A method of estimating the magnitude of shot-noise effects on the deprojected velocity field is derived. We find that there is a good correlation between the true and deprojected density and velocity fields, even in the mildly non-linear regime, provided that on large scales galaxies trace the mass. An initial application is made to the IRAS-QDOT all-sky redshift survey.