Single Frequency CMB Foreground Removal with Inter-scale Machine Learning

Abstract

Accurate measurements of Cosmic Microwave Background (CMB) B-mode polarization, a key probe of inflationary physics, are hindered by complex Galactic dust foregrounds. Traditional foreground removal with Internal Linear Combination (ILC) fully preserves the primordial signal but requires multi-frequency data and is limited to two-point statistics. We present a novel way to estimate and remove foregrounds at single frequency using signal-preserving machine learning that leverages inter-scale correlations. Using the DustFilaments simulations, we train CNNs to reconstruct large-scale foregrounds (ℓ < 200) from small-scales (ℓ > 200). We quantify the effectiveness of foreground removal with the residual foreground power, f_resid, which gives the fraction of foreground power remaining after removal. Predictions using only small-scale B-modes achieve f_resid≃ 0.704, while adding temperature and E-modes decreases it to f_resid ≃ 0.376. These results are still higher than the spatial ILC, which leverages multi-frequency data at Simons-Observatory-like frequencies. However, a hybrid network that uses both multi-frequency and inter-scale correlations attains f_resid=4.71×10⁻⁴ when using B-mode inputs alone, and 3.62×10⁻⁴ when using temperature and E/B-mode inputs. This network achieves a residual power of ∼ 7× lower than ILC, while inheriting ILC's signal-preserving property. This is ∼ 2--3× lower than a network that only uses multi-frequency inputs, demonstrating that correlations across scale are not redundant with correlations across frequency and that our techniques are complementary to multi-frequency foreground removal. However, this is achieved only for DustFilments and network generalization across simulations remains a key challenge for robust ML-based foreground removal. (abridged)

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Cite

BibTeX RIS

BibTeX

@misc{shao2026single,
  title = {{Single Frequency CMB Foreground Removal with Inter-scale Machine Learning}},
  author = {Helen Shao and Fiona McCarthy and Blake D. Sherwin and Miles Cranmer and Carlos Hervias-Caimapo},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2607.28712},
  eprint = {2607.28712},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.28712},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Single Frequency CMB Foreground Removal with Inter-scale Machine Learning
AU  - Helen Shao
AU  - Fiona McCarthy
AU  - Blake D. Sherwin
AU  - Miles Cranmer
AU  - Carlos Hervias-Caimapo
PY  - 2026
DA  - 2026/11/04
PB  - arXiv
DO  - 10.48550/arxiv.2607.28712
UR  - https://arxiv.org/abs/2607.28712
AB  - Accurate measurements of Cosmic Microwave Background (CMB) B-mode polarization, a key probe of inflationary physics, are hindered by complex Galactic dust foregrounds. Traditional foreground removal with Internal Linear Combination (ILC) fully preserves the primordial signal but requires multi-frequency data and is limited to two-point statistics. We present a novel way to estimate and remove foregrounds at single frequency using signal-preserving machine learning that leverages inter-scale correlations. Using the DustFilaments simulations, we train CNNs to reconstruct large-scale foregrounds (ℓ < 200) from small-scales (ℓ > 200). We quantify the effectiveness of foreground removal with the residual foreground power, f_resid, which gives the fraction of foreground power remaining after removal. Predictions using only small-scale B-modes achieve f_resid≃ 0.704, while adding temperature and E-modes decreases it to f_resid ≃ 0.376. These results are still higher than the spatial ILC, which leverages multi-frequency data at Simons-Observatory-like frequencies. However, a hybrid network that uses both multi-frequency and inter-scale correlations attains f_resid=4.71×10^−4 when using B-mode inputs alone, and 3.62×10^−4 when using temperature and E/B-mode inputs. This network achieves a residual power of ∼ 7× lower than ILC, while inheriting ILC's signal-preserving property. This is ∼ 2--3× lower than a network that only uses multi-frequency inputs, demonstrating that correlations across scale are not redundant with correlations across frequency and that our techniques are complementary to multi-frequency foreground removal. However, this is achieved only for DustFilments and network generalization across simulations remains a key challenge for robust ML-based foreground removal. (abridged)
ER  -

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