Wiener Reconstruction, SVD and ‘Optimal Functional Bases: Application For Redshift Galaxy Catalogs

The formalism of Wiener filtering is applied to reconstruct, in terms of spherical harmonics, the projected $4\pi$ 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.
Comment: To appear in the proceedings of the XXXth MORIOND meeting: "Clustering in the Universe". 6 pages, 4 figures included; uuencoded, compressed PostScript file