Foreground removal in HI 21 cm intensity mapping under frequency-dependent beam distortions

Context. Neutral hydrogen (HI) intensity mapping with single-dish experiments is a powerful approach for probing cosmology in the post-reionization epoch. It is challenging to extract it, however, because of the bright foregrounds, which are stronger than the HI signal by more than four orders of magnitude. While all methods perform well when a Gaussian beam is assumed that is degraded to the lowest resolution, most methods degrade significantly in a more realistic beam model. Aims. The complexity introduced by frequency-dependent beam effects means that we need methods that explicitly account for the instrument response. We investigate the performance of SDecGMCA. This method extends DecGMCA to spherical data by combining sparse component separation with beam deconvolution. Our goal is to evaluate this method in comparison with established foreground removal techniques by assessing its ability to recover the cosmological HI signal from single-dish intensity mapping observations under varying beam conditions. Methods. We used simulated HI signals and foregrounds informed by existing observational and theoretical models that cover the frequency ranges relevant to MeerKAT and SKA-Mid. The foreground removal techniques we tested fall into two main categories: model-fitting methods (polynomial and parametric), and blind source separation methods (PCA, ICA, GMCA, and SDecGMCA). Their effectiveness was evaluated based on the recovery of the HI angular and frequency power spectra under progressively more realistic beam conditions. Results. While all methods performed adequately under a uniform degraded beam, SDecGMCA remained robust when frequency-dependent beam distortions were introduced. For an oscillating beam, SDecGMCA suppressed the spurious spectral peak at kν ∼ 0.3 and achieved an accuracy of ≲5% at intermediate angular scales (10 < ℓ < 200); it outperformed other methods. Furthermore, the masking of bright Galactic regions significantly improved the recovery of the HI signal, in particular, for SDecGMCA, which benefited most when contaminated lines of sight were excluded. The beam inversion, however, remained intrinsically unstable beyond ℓ ∼ 200. This sets a practical limit on the method. Conclusions. Our findings highlight the limitations of simple fitting and standard blind source separation methods for realistic beam effects, and they establish SDecGMCA as a particularly promising approach for future single-dish intensity mapping surveys. Its robustness for various beam models, combined with the improvements that can be achieved through masking strategies and forthcoming refinements to its thresholding scheme, suggest that SDecGMCA might provide reliable spherical harmonics reconstructions of the HI power spectrum in upcoming experiments.