Abstract The Generalized Needlet Internal Linear Combination (GNILC) method is a nonparametric component separation algorithm to remove the foreground contamination of the 21 cm intensity mapping data. In this work, we perform the discrete cosine transform along the frequency axis in the expanded GNILC framework (denoted eGNILC), which helps reduce the power loss in low multipoles, and further demonstrates its performance. We also calculate the eGNILC bias to modify the criterion for determining the degrees of freedom (dof) of the foreground, and embed the robust principal component analysis in mixing matrix computation to obtain a blind component separation method. We find that the eGNILC bias is related to the averaged domain size and the dof of the foreground but not the underlying 21 cm signal. In the case of no beam effect, the eGNILC bias is negligible for simple power-law foregrounds outside the Galactic plane. We also examine the eGNILC performance in the SKA Phase-I in mid-frequency (SKA-MID) and Baryon Acoustic Oscillations from Integrated Neutral Gas Observations (BINGO) simulations. We show that if the adjacent frequency channels are not highly correlated, eGNILC can recover the underlying 21 cm signal with good accuracy. With the varying Airy-disk beam applied to both SKA-MID and BINGO, the power spectra of 21 cm can be effectively recovered at the multipoles ℓ ∈ [20, 250] and [20, 300], respectively. With no instrumental noise, the SKA-MID exhibits ≲20% power loss, and BINGO exhibits ~10% power loss. The varying Airy-disk beam only causes significant errors at large multipoles.
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