Foreground Removal in Ground-Based CMB Observations Using a Transformer Model

TL;DR

This work introduces TCMB, a Transformer-based method that processes HEALPix spherical maps to remove Galactic foregrounds from ground-based CMB polarization data. By partitioning full-sky maps into patches and employing Swin Transformer blocks, TCMB achieves robust foreground removal and preserves CMB signal and instrumental noise, validated through cross-correlation of half-mission maps to debias noise. Compared with a CNN baseline, TCMB shows superior map-level recovery and avoids boundary artefacts intrinsic to flat-sky projections, though generalization hinges on foreground-model diversity in training. The results imply a significant potential for Transformer-based approaches in CMB data analysis and broader applications on spherical data domains.

Abstract

We present a novel method for Cosmic Microwave Background (CMB) foreground removal based on deep learning techniques. This method employs a Transformer model, referred to as \texttt{TCMB}, which is specifically designed to effectively process HEALPix-format spherical sky maps. \texttt{TCMB} represents an innovative application in CMB data analysis, as it is an image-based technique that has rarely been utilized in this field. Using simulated data with noise levels representative of current ground-based CMB polarization observations, the \texttt{TCMB} method demonstrates robust performance in removing foreground contamination. The mean absolute variance for the reconstruction of the noisy CMB Q/U map is significantly less than the CMB polarization signal. To mitigate biases caused by instrumental noise, a cross-correlation approach using two half-mission maps was employed, successfully recovering CMB EE and BB power spectra that align closely with the true values, and these results validate the effectiveness of the \texttt{TCMB} method. Compared to the previously employed convolutional neural network (CNN)-based approach, the \texttt{TCMB} method offers two significant advantages: (1) It demonstrates superior effectiveness in reconstructing CMB polarization maps, outperforming CNN-based methods. (2) It can directly process HEALPix spherical sky maps without requiring rectangular region division, a step necessary for CNN-based approaches that often introduces uncertainties such as boundary effects. This study highlights the potential of Transformer-based models as a powerful tool for CMB data analysis, offering a substantial improvement over traditional CNN-based techniques.

Figures (15)

• Figure 1: Inverse standard deviation of the polarization noise at frequencies of 95 GHz and 150 GHz, calculated at a resolution of $\rm N_{side}=1024$.The gray line indicates the boundaries of the UNP mask.
• Figure 2: Orthographic view of the HEALPix partition of the sphere. The resolution parameter of the map is set to NSIDE=8. The black points and lines represent the center positions and boundaries of the map pixels, respectively. The red lines denote the boundaries of the defined patch, which has its size parameter set to ${\rm \texttt{NSIDE}_P}=2$.
• Figure 3: The network architecture for TCMB.
• Figure 4: The results of foreground removal using TCMB method at map level. The upper panels illustrate the recovery of the Q map, while the lower panels depict the recovery of the U map. The simulated maps are a beam-convolved CMB map plus a noise map at a frequency of 95 GHz. The recovered maps correspond to the noisy CMB maps that were recovered using the TCMB method from multi-band observational data. The residual maps indicate the differences between the recovered map and the target map.
• Figure 5: Recovered power spectra of the E-mode (EE) and B-mode (EE) of the CMB, incorporating contributions from noise. The simulated power spectra were calculated from the beam-convolved CMB map plus a noise map at a frequency of 95 GHz. The recovered power spectra were derived from the noisy CMB maps, which were obtained through the application of the TCMB method on multi-band observational data. $\Delta D_{\ell}$ represents the difference between the recovered power spectrum and the target power spectrum, $\Delta D_{\ell}= D_{\ell ,\rm recovered} - D_{\ell, \rm true}$. The black dashed lines represent the power spectra calculated using the pure CMB map. The length of each $\ell$ bin is set to be 30.