21-cm foreground removal using AI and the frequency-difference technique

The deep learning technique has been employed in removing foreground contaminants from 21-cm intensity mapping, but its effectiveness is limited by the large dynamic range of the foreground amplitude. In this study, we develop a novel foreground removal technique grounded in U-Net networks. The essence of this technique lies in introducing an innovative data preprocessing step specifically, utilizing the temperature difference between neighboring frequency bands as input. Combining with the frequency difference, we refer to our method as the UNet-fd (UNet frequency-difference), where the U-Net structure is the same as that in deep21. Based on our tests, we demonstrate that this frequency-difference preprocessing technique can substantially reduce the dynamic range of foreground amplitudes by approximately two orders of magnitude. This reduction proves to be highly advantageous for the U-Net foreground removal. We observe that the HI signal can be reliably recovered, as indicated by the cross-correlation power spectra showing unity agreement at the scale of $k\lesssim 0.3h{\mathrm{Mpc}}^{-1}$ in the absence of instrumental effects. Moreover, accounting for the systematic beam effects, our reconstruction displays consistent autocorrelation and cross-correlation power spectrum ratios at the $1\sigma$ level across scales $k\lesssim 0.1h{\mathrm{Mpc}}^{-1}$, with only a 10% reduction observed in the cross-correlation power spectrum at $k\simeq 0.2h{\mathrm{Mpc}}^{-1}$. The effects of redshift-space distortion are also reconstructed successfully, as evidenced by the quadrupole power spectra matching with the target truth. In order to test how thermal noise affects the performance of our method, we simulated various white noise levels in the map. This shows the mean cross-correlation ratio ${\overline{R}}_{\text{cross}}\gtrsim 0.8$ when the level of the thermal noise is smaller than or equal to that of the HI signal. In comparison, our method outperforms the traditional principal component analysis (PCA) method. The PCA-derived cross-correlation ratios are underestimated by around 60%. We conclude that the proposed frequency-difference technique can significantly enhance network performance by reducing the amplitude range of foregrounds and aiding in the prevention of HI loss.