Bayesian analysis of spatially distorted cosmic signals from Poissonian data

Abstract

Reconstructing the matter density field from galaxy counts is a problem frequently addressed in current literature. Two main sources of error are shot noise from galaxy counts and insufficient knowledge of the correct galaxy position because of peculiar velocities and redshift measurement uncertainty. Here, we address the reconstruction problem of a Poissonian sampled lognormal density field with velocity distortions in a Bayesian way using a maximum a posteriori method. We test our algorithm on a one-dimensional test case and find significant improvement compared to simple data inversion. In particular, we address the following problems: photometric redshifts, mapping of extended sources in coded mask systems, real space reconstruction from redshift space galaxy distribution and combined analysis of data with different point spread functions. © 2010 The Authors. Journal compilation © 2010 RAS.