Abstract
Extracting a sky map of the Cosmic Microwave Background (CMB) from multi-channel measurements can be seen as a component separation problem in a special context: only one component is of interest (the CMB) and its column in the mixing matrix and its probability distribution are known with high accuracy. The purpose of this paper is not to present a new algorithm but rather to discuss, on a purely theoretical basis, the impact of the statistical modeling of the components in a simple case. To do so, we analyze a model of noise-free CMB observations contaminated by coherent components. We show that the maximum likelihood estimate of the CMB in this model does not depend of the model of the contamination.
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Notes
- 1.
Of course, such a \({\mathbf {w}}{^\dagger }\) would then be nothing else than the first row of \({{\mathbf {A}}}{^{-1}}\).
- 2.
The pre-processing \({{\mathbf {P}}}\) is only introduced here as a ‘mathematical device’ but a similar idea is actually implemented in the SEVEM algorithm for CMB extraction [3].
References
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Cardoso, JF. (2017). On Extracting the Cosmic Microwave Background from Multi-channel Measurements. In: Tichavský, P., Babaie-Zadeh, M., Michel, O., Thirion-Moreau, N. (eds) Latent Variable Analysis and Signal Separation. LVA/ICA 2017. Lecture Notes in Computer Science(), vol 10169. Springer, Cham. https://doi.org/10.1007/978-3-319-53547-0_38
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DOI: https://doi.org/10.1007/978-3-319-53547-0_38
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