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

Abstract

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