Application of Physics-Informed Neural Networks in Removing Telescope Beam Effects

This study introduces {\tt{PI-AstroDeconv}}, a physics-informed semi-supervised learning method specifically designed for removing beam effects in astronomical telescope observation systems. The method utilizes an encoder-decoder network architecture and combines the telescope's point spread function or beam as prior information, while integrating fast Fourier transform accelerated convolution techniques into the deep learning network. This enables effective removal of beam effects from astronomical observation images. {\tt{PI-AstroDeconv}} can handle multiple PSFs or beams, tolerate imprecise measurements to some extent, and significantly improve the efficiency and accuracy of image deconvolution. Therefore, this architecture is particularly suitable for astronomical data processing that does not rely on annotated data. To validate the reliability of the architecture, we used the SKA Science Data Challenge 3a datasets and compared it with the $\tt{CLEAN}$ deconvolution method at the 21-cm power spectrum level. The results demonstrate that our algorithm not only restores details and reduces blurriness in celestial images at the pixel level but also more accurately recovers the true neutral hydrogen power spectrum at the power spectrum level.