Maximum Likelihood algorithm for parametric component separation in CMB experiments

Understand

We discuss an approach to the component separation of microwave, multi-frequency sky maps as those typically produced from Cosmic Microwave Background (CMB) Anisotropy data sets.

• The algorithm is based on the two step, parametric, likelihood-based technique recently elaborated on by Eriksen et al., (2006), where the foreground spectral parameters are estimated prior to the actual separation of the components.
• In contrast with the previous approaches, we accomplish the former task with help of an analytically-derived likelihood function for the spectral parameters, which, we show, yields estimates equal to the maximum likelihood values of the full multi-dimensional data problem.
• We then use these estimates to perform the second step via the standard, generalized-least-square-like procedure.