A linear filter to reconstruct the ISW effect from CMB and LSS observations

TL;DR

This paper introduces a linear covariance-based filter that improves the reconstruction of the ISW effect by utilizing correlations between CMB and galaxy observations, outperforming traditional methods.

Contribution

The paper presents a novel linear filter that incorporates additional correlated observations to enhance signal extraction in astrophysical data analysis.

Findings

The filter effectively reconstructs the ISW signal from simulated data.

It outperforms traditional Wiener filtering in accuracy.

The method demonstrates potential for improved cosmological signal recovery.

Abstract

The extraction of a signal from some observational data sets that contain different contaminant emissions, often at a greater level than the signal itself, is a common problem in Astrophysics and Cosmology. The signal can be recovered, for instance, using a simple Wiener filter. However, in certain cases, additional information may also be available, such as a second observation which correlates to a certain level with the sought signal. In order to improve the quality of the reconstruction, it would be useful to include as well this additional information. Under these circumstances, we have constructed a linear filter, the linear covariance-based filter, that extracts the signal from the data but takes also into account the correlation with the second observation. To illustrate the performance of the method, we present a simple application to reconstruct the so-called Integrated Sachs-Wolfe effect from simulated observations of the Cosmic Microwave Background and of catalogues of galaxies.