Constrained realizations and minimum variance reconstruction of non - Gaussian random elds

With appropriate modi cations, the Ho man{Ribak algorithm that constructs constrained realizations of Gaussian random elds having the correct ensemble properties can also be used to construct constrained realizations of those non-Gaussian random elds that are obtained by transformations of an underlying Gaussian eld. For example, constrained realizations of lognormal, generalized Rayleigh, and chi-squared elds having n degrees of freedom constructed this way will have the correct ensemble properties. The lognormal eld is considered in detail. For reconstructing Gaussian random elds, constrained realization techniques are similar to reconstructions obtained using minimum variance techniques. A comparison of this constrained realization approach with minimum variance, Wiener lter reconstruction techniques, in the context of lognormal random elds, is also included. The resulting prescriptions for constructing constrained realizations as well as minimumvariance reconstructions of lognormal random elds are useful for reconstructing masked regions in galaxy catalogues on smaller scales than previously possible, for assessing the statistical signi cance of small-scale features in the microwave background radiation, and for generating certain non-Gaussian initial conditions for N -body simulations.