A statistical analysis of the “internal linear combination” method in problems of signal separation as in cosmic microwave background observations

¹ Chip Computers Consulting s.r.l., Viale Don L. Sturzo 82, S.Liberale di Marcon, 30020 Venice, Italy e-mail: robertovio@tin.it,
² ESO, Karl Schwarzschild strasse 2, 85748 Garching, Germany
³ INAF - Osservatorio Astronomico di Trieste, via Tiepolo 11, 34143 Trieste, Italy e-mail: pandrean@eso.org

Received: 2 January 2008
Accepted: 26 May 2008

Abstract

Aims. The separation of foreground contamination from cosmic microwave background (CMB) observations is one of the most challenging and important problems of digital signal processing in Cosmology. In the literature, various techniques have been presented but no general consensus about their real performance and properties has been reached. This is due to the characteristics of these techniques that have been studied essentially through numerical simulations based on semi-empirical models of the CMB and the Galactic foreground. Such models often have different levels of sophistication and/or are based on different physical assumptions (e.g. the number of Galactic components and level of the noise). Hence, a reliable comparison is difficult. What is missing is a statistical analysis of the properties of the proposed methodologies. Here, we consider the Internal Linear Combination method (ILC) which, among the separation techniques, requires the smallest number of a priori assumptions. This feature is of particular interest in the context of CMB polarization measurements at small angular scales where the lack of knowledge of the polarized backgrounds represents a serious limit.

Methods. The statistical characteristics of ILC are examined through an analytical approach and the basic conditions are fixed so as to work satisfactorily.

Results. ILC provides satisfactory results only under rather restrictive conditions. This is a critical fact to take into consideration in planning future ground-based observations (e.g., with ALMA) where, contrary to satellite experiments, there is the possibility of having a certain control over the experimental conditions.