Single Frequency CMB Foreground Removal with Inter-scale Machine Learning

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 (< 200) from small-scales (> 200). We quantify the effectiveness of foreground removal with the residual foreground power, f, which gives the fraction of foreground power remaining after removal. Predictions using only small-scale B-modes achieve f 0.704, while adding temperature and E-modes decreases it to f 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=4.71 times10-4 when using B-mode inputs alone, and 3.62 times10-4 when using temperature and E/B-mode inputs. This network achieves a residual power of about 7 times lower than ILC, while inheriting ILC's signal-preserving property. This is about 2 -- 3 times 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)