Foreground Mitigation in Cosmological 21 cm Observations: From Component Separation to End-to-End Inference

Redshifted 21 cm observations can trace neutral hydrogen from Cosmic Dawn and the Epoch of Reionization to lower-redshift large-scale structure, but foreground emission exceeds the cosmological fluctuations by several orders of magnitude. This review follows foreground mitigation from the measurement equation to final validation. We summarize spectral fitting, PCA/SVD, ICA, KL methods, GPR, GMCA, and DAYENU, including their signal loss in an idealized comparison. We then show how chromatic beams and frequency-dependent interferometric sampling mix angular foreground structure into line-of-sight modes and form the foreground wedge. Bayesian forward models and deep networks are assessed as routes to field and power-spectrum inference when the telescope response is included. Drawing on the SKA Science Data Challenge 3a, we summarize the experience gained and lessons learned, with emphasis on practical challenges in data processing, signal recovery, and uncertainty estimation. We conclude with field-level validation based on cross-correlation, transfer functions, and recovered power spectra.