Component Separation Methods
Sky o​bservations at submillimetre and radio frequencies contain a complex mixture of Galactic and extragalactic emissions accumulated over cosmic history. Astrophysical foregrounds in the nearby Universe, such as Galactic emissions from our own Galaxy, obscure much of the cosmological information in the early Universe, such as that carried by the cosmic microwave background (CMB). This poses a key challenge in cosmology, known as the component separation problem (see Delabrouille & Cardoso, 2007 for a review): How to disentangle cosmological signals of primordial origin from astrophysical foregrounds in multi-frequency sky observations? I have developed several component separation methods in cosmology, which are listed below.​​
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(Click on paper's title to access the corresponding publication)
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CILC (Constrained ILC)
CMB and SZ effect separation with constrained Internal Linear Combinations
Remazeilles, Delabrouille, Cardoso, MNRAS 410, 2481 (2011)
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In this paper, we introduced a new component separation method called "Constrained ILC" (CILC), which extends the standard internal linear combination (ILC) approach by adding deprojection constraints. This allows specific foregrounds with known frequency spectra, such as the thermal SZ emission from galaxy clusters, to be nulled out in the reconstructed CMB map.
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By eliminating thermal SZ clusters from the CMB map, this method is particularly well suited for extracting the kinetic SZ effect (e.g., Planck intermediate results XIII, A&A 2014; Planck intermediate results LIII, A&A 2018; Li et al., PRD 2018), for cross-correlations with large-scale structure surveys (e.g., Chen et al., MNRAS 2018; Chen & Remazeilles, MNRAS 2022), or for primordial non-Gaussianity searches (e.g. Hill, PRD 2018). CILC has also been applied to new areas of cosmology, such as the extraction of the relativistic SZ effect (Remazeilles & Chluba, MNRAS 2020, 2025) and μ-type spectral distortion anisotropies (Remazeilles & Chluba, MNRAS 2018; Remazeilles et al., MNRAS 2022). More broadly, the CILC method has been widely adopted by the CMB community, including the ACT and SO collaborations (e.g., Madhavacheril et al., PRD 2020; Coulton et al., PRD 2024), to mitigate extragalactic foregrounds in CMB data.
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GNILC (Generalized Needlet Internal Linear Combination)
​Foreground separation with generalized Internal Linear Combinations
Remazeilles, Delabrouille, Cardoso, MNRAS 418, 467 (2011)​​
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In this paper, we developed GNILC, a multi-dimensional extension of the ILC method designed to reconstruct correlated, multi-component emissions such as Galactic foregrounds and the cosmic infrared background (CIB). Its key innovation is to exploit statistical properties where spectral information is poorly known or degenerate, enabling it to disentangle components suffering from spectral degeneracy (i.e., with similar frequency spectra), such as Galactic dust and CIB.
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A major breakthrough with GNILC was the first successful separation of Galactic thermal dust from extragalactic CIB emission in Planck data (Planck intermediate results XLVIII, A&A 2016). It was later adopted as one of only five component separation methods recognised by the Planck consortium (Planck 2018 results IV, A&A 2020) and played a central role in several further Planck studies, including the characterization of Galactic dust polarization (Planck 2018 results XII, A&A 2020) and CMB delensing using GNILC CIB maps (Planck 2018 results VIII, A&A 2020). GNILC was also applied to revisit Planck’s Galactic CO maps, significantly reducing noise and systematics (Ghosh, Remazeilles & Delabrouille, A&A 2024).
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Beyond Planck, GNILC was extended to line intensity mapping, enabling extraction of the cosmological 21-cm hydrogen line emission (Olivari, Remazeilles & Dickinson, MNRAS 2016). It has been successfully applied to forecast the performance of future radio telescopes such as BINGO (Fornazier et al., A&A 2022; de Mericia et al., A&A 2023) and SKAO (De Caro et al., 2025).​​​
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cMILC (Constrained Moment ILC)
Peeling off foregrounds with the constrained moment ILC method to unveil primordial CMB B-modes
Remazeilles, Rotti, Chluba, MNRAS 503, 2478 (2021)
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By combining statistical moment expansion of the foreground emission (Chluba et al., MNRAS 2017) with the constrained ILC method (Remazeilles et al., MNRAS 2011), we introduced a new map-based, semi-blind component separation method, cMILC ("Constrained Moment ILC"), to handle foreground spectral distortions beyond the leading-order SED, arising from the integration of multiple spectral contributions along and across the lines of sight. At the intersection of blind and parametric approaches, cMILC enables the deprojection of the main foreground moments caused by line-of-sight integration and beam convolution, significantly reducing residual foreground contamination in the recovery of the primordial CMB B-mode polarization signal. In LiteBIRD Collaboration forecasts, cMILC has been shown to outperform the standard NILC (Needlet ILC) method for tensor-to-scalar ratio recovery (Fuskeland et al., A&A 2023).
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ocMILC (Optimized Constrained Moment ILC)
Optimization of foreground moment deprojection for semi-blind CMB polarization reconstruction
Carones & Remazeilles, JCAP 06, 018 (2024)
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Although the CILC (Remazeilles et al., MNRAS 2011) and cMILC (Remazeilles et al., MNRAS 2021) methods improve foreground subtraction through deprojection constraints, this comes at the cost of increased overall noise due to the trade-off between foreground bias reduction and overall variance minimization. Considering that some foreground moments are better suited for deprojection, while others are better handled via blind variance minimization, we introduced the optimized cMILC (ocMILC) pipeline, which builds upon cMILC by adaptively selecting the number and type of foreground moments to deproject based on sky complexity, frequency coverage, and experimental sensitivity. This data-driven approach enhances foreground subtraction while minimizing the associated noise penalty.
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Hybrid ILC
Remazeilles, arXiv:2507.22109 (2025)
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Cosmic birefringence—arising from potential parity-violating interactions between CMB photons and pseudo-scalar fields like axion-like particles—rotates the polarization plane of the CMB, inducing correlations between CMB E- and B-mode polarization. In this paper, we introduced the Hybrid ILC method, which constructs a hybrid CMB E-mode polarization map by jointly combining both E- and B-mode frequency maps with frequency-dependent weights, allowing us to disentangle the correlated and uncorrelated components of the CMB E-mode field. This enables direct linear regression across the sky between the correlated component of the CMB E-mode and the full CMB B-mode field to estimate the birefringence angle.
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The Hybrid ILC technique offers promising avenues for future component separation. By combining temperature and polarization channels, it can help disentangle spectrally degenerate signals, such as CMB vs. kinetic SZ or thermal dust vs. CIB, using the intrinsic TE correlation to reduce the sample variance from the polarized component in the unpolarized signal. It can also improve the cleaning of Galactic foregrounds in unpolarized extragalactic signals, such as 21-cm line intensity maps.
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