Non-linear Reconstruction of the Large Scale Structure

The linear algorithm of the the full non-linear large scale structure of Gaussian random fields is extended here to to perform non-linear CRs. The procedure consists of: (1) Using linear CR of low resolution data to construct a high resolution realization of the underlying field, as if the linear theory is valid; (2) Taking the linear CR backwards in time, by the linear theory, to set initial conditions for an N-body simulation; (3) Forwarding the field in time by an N-body code. An intermediate step might be introduced to `linearize' the low resolution data. The non-linear CR can be applied to any observational data set that is linearly related to the underlying field. Here it is applied to the IRAS 1.2Jy catalog using 843 data points within a sphere of $6000 Km/s$, to reconstruct the full non-linear large scale structure of our `local' universe.