  The linear algorithm of the Wiener filter and constrained realizations (CRs)
of Gaussian random fields is extended here to perform non-linear CRs. The
procedure consists of: (1) Using low resolution data to constrain 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 N-body simulations; (3) Forwarding the field in time by
an N-body code. An intermediate step is introduced to `linearize' the low
resolution data. The non-linear CR can be applied to any observational data set
that is quasi-linearly related to the underlying field. Here it is applied to
the IRAS 1.2Jy catalog using 846 data points within a sphere of 6000 km/s, to
reconstruct the full non-linear large scale structure of our `local' universe.
The method is tested against mock IRAS surveys, taken from random non-linear
realizations. A detaile analysis of the reconstructed non-linear structure is
presented.
