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Cosmology and Nongalactic Astrophysics · arXiv:2308.03412 v2 · submitted 7 Aug 2023

Non-parametric maximum likelihood component separation for CMB polarization data

Clément Leloup, Josquin Errard, Radek Stompor

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“However, we also show that much less stringent assumptions are sufficient if we only aim at recovering the cleaned CMB signal.”

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Abstract

Mitigation of the impact of foreground contributions to measurements of Cosmic Microwave Background (CMB) polarization is a crucial step in modern CMB data analysis and is of particular importance for a detection of large-scale CMB B modes. A large variety of techniques, based on different assumptions and aiming at either a full component separation or merely cleaning the foreground signals from the CMB maps, have been described in the literature. In this work, we consider this problem within a unified framework based on the maximum likelihood principle, under the assumption that the signal at each frequency can be represented as a linear mixture of sky templates. We discuss the impact of various additional assumptions on the final outcome of the procedure. We find that the component separation problem can be fully solved in two specific situations: when we either know the frequency scaling of all the components or can correctly model them with a limited number of unknown parameters, as is the case in the parametric component separation techniques; or when we either know the statistical properties of all the components, the foregrounds and CMB, or can correctly model them with a limited number of parameters, as for instance in SMICA-like approaches. However, we also show that much less stringent assumptions are sufficient if we only aim at recovering the cleaned CMB signal. In particular, we discuss a “minimally informed” non-parametric method based on maximum likelihood. The method only assumes that the component properties are independent on the sky direction, at least over some region of the sky, and that the CMB covariance is known up to some limited number of parameters. We apply this method to recover the CMB B modes polarization signal in the context of forthcoming CMB experiments and compare its performance with that of the standard parametric... (abridged)

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abstract compiled · 2026-09-23 · no language-model review

How the main claim is stated: asserted 0.99

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.64 · human participants 0.01 · controlled comparison 0.47 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.94 · mentions code or data availability 0.02

The abstract, sentence by sentence

This table labels the abstract only (arXiv listing abstract v2). The number is the probability the classifier gave the label.

SentenceRoleThe authors' own workStates the main conclusionStrength
Mitigation of the impact of foreground contributions to measurements of Cosmic Microwave Background (CMB) polarization is a crucial step in modern CMB data analysis and is of particular importance for a detection of large-scale CMB $B$ modes. background 1.00 0.04 0.03 asserted 1.00
A large variety of techniques, based on different assumptions and aiming at either a full component separation or merely cleaning the foreground signals from the CMB maps, have been described in the literature. background 1.00 0.03 0.02 asserted 0.99
In this work, we consider this problem within a unified framework based on the maximum likelihood principle, under the assumption that the signal at each frequency can be represented as a linear mixture of sky templates. method 0.89 0.78 0.05 asserted 0.91
We discuss the impact of various additional assumptions on the final outcome of the procedure. contribution 0.58 0.76 0.04 unclear 0.61
We find that the component separation problem can be fully solved in two specific situations: when we either know the frequency scaling of all the components or can correctly model them with a limited number of unknown parameters, as is the case in the parametric component separation techniques; or when we either know the statistical properties of all the components, the foregrounds and CMB, or can correctly model them with a limited number of parameters, as for instance in SMICA-like approaches. result 0.98 0.87 0.33 asserted 1.00
However, we also show that much less stringent assumptions are sufficient if we only aim at recovering the cleaned CMB signal. result 0.91 0.89 0.34 asserted 0.99
In particular, we discuss a ``minimally informed'' non-parametric method based on maximum likelihood. method 0.54 0.84 0.16 asserted 0.94
The method only assumes that the component properties are independent on the sky direction, at least over some region of the sky, and that the CMB covariance is known up to some limited number of parameters. method 0.98 0.64 0.15 asserted 0.94
We apply this method to recover the CMB $B$ modes polarization signal in the context of forthcoming CMB experiments and compare its performance with that of the standard parametric... (abridged) contribution 0.63 0.93 0.09 asserted 0.90

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 0.64

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How the labels were made

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 7,095 input tokens.

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. This record as JSON

Cited by 1 Pith paper

Reviewed papers on Pith that cite this one. The full citation record

  1. Robust paths to primordial $B$ modes in the presence of polarised point source contamination astro-ph.CO · Oct 2026
How the literature uses it

3 arXiv papers cite this in 26 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 14 sentences without a confident label

Builds on it 1 paper
  • This paper describes a pixel domain reformulation and implementation of the Leloup et al. (2023) [ref] formalism proposing a new component separation framework potentially better adapted to dealing with realistic foreground emissions, including their frequency and spatial behaviors, in the context of upcoming CMB observations.

    Pixel domain implementation of the Minimally Informed CMB MAp foreground Cleaning method · Introduction · 0.85

Uses its method or tool 2 papers
Compares with it 1 paper
Cites it as support 1 paper
Cites it as background 2 papers

What it cites · 21 sentences without a confident label

Uses the method or tool of 4 papers
Compares with 2 papers
Cites as support 4 papers
Cites as background 13 papers
  • Among others, the most extensively studied are based on the empirical modeling of the foreground SEDs in parametric methods [ref] , on statistical properties of the foreground in the Internal Linear Combination (ILC) [ref] and Independent Component Analysis (ICA) [ref] techniques, and on the definition of internal or external foreground templates in template fitting methods [ref] .

    Component separation with flexible models. Application to the separation of astrophysical emissions · Introduction · 0.94

  • Among others, the most extensively studied are based on the empirical modeling of the foreground SEDs in parametric methods [ref] , on statistical properties of the foreground in the Internal Linear Combination (ILC) [ref] and Independent Component Analysis (ICA) [ref] techniques, and on the definition of internal or external foreground templates in template fitting methods [ref] .

    Maximum Likelihood algorithm for parametric component separation in CMB experiments · Introduction · 0.94

  • Among others, the most extensively studied are based on the empirical modeling of the foreground SEDs in parametric methods [ref] , on statistical properties of the foreground in the Internal Linear Combination (ILC) [ref] and Independent Component Analysis (ICA) [ref] techniques, and on the definition of internal or external foreground templates in template fitting methods [ref] .

    A Statistical Analysis of the "Internal Linear Combination" Method in Problems of Signal Separation as in CMB Observations · Introduction · 0.94

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