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 ($\ell < 200$) from small-scales ($\ell > 200$). We quantify the effectiveness of foreground removal with the residual foreground power, $f_{\rm{resid}}$, which gives the fraction of foreground power remaining after removal. Predictions using only small-scale $B$-modes achieve $f_{\rm{resid}}\simeq 0.704$, while adding temperature and $E$-modes decreases it to $f_{\rm{resid}} \simeq 0.376$. 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 $f_{\rm{resid}}=4.71\times10^{-4}$ 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 $\sim 7\times$ lower than ILC, while inheriting ILC's signal-preserving property. This is $\sim 2$--$3\times$ 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)