Wiener reconstruction, SVD and `Optimal' Functional bases: Appliction For Redshift Galaxy Catalogs

Abstract

The formalism of Wiener filtering is applied to reconstruct, in terms of spherical harmonics, the projected $4π$ galaxy distribution of a mock IRAS 1.2 Jy catalog with a `Zone of Avoidance' $|b| = 15^\circ$. The Singular Value Decomposition al gorithm is utilized as an extra-regularizer in order to stabilize the inversion. This case sheds light on the amount of useful information contained in the data, and also suggests a method for obtaining an `optimal' functional basis, based on our \prior knowledge, for the purposes of likelihood analysis and Wiener reconstruction of cosmological data sets. The applicability of such a functional basis for redshift galaxy catalogs is also discussed.