Power filtration of CMB observational data

We propose a power filter Cp for linear reconstruction of the CMB signal from one-dimensional scans of observational maps. This Gp filter preserves the power spectrum of the CMB signal in contrast to the Wiener filter which diminishes the power spectrum of the reconstructed CMB signal. We demonstrate how peak statistics and a cluster analysis can be used to estimate the probability of the presence of a CMB signal in observational records.

The efficiency of the G, filter is demonstrated on a toy model of an observational record consisting of a CMB signal and noise in the form of foreground point sources.