A Semi-blind PCA-based Foreground Subtraction Method for 21 cm Intensity Mapping

The Principal Component Analysis (PCA) method and the Singular Value Decomposition (SVD) method are widely used for foreground subtraction in 21 cm intensity mapping experiments. We show their equivalence, and point out that the condition for completely clean separation of foregrounds and cosmic 21 cm signal using the PCA/SVD is unrealistic. We propose a PCA-based foreground subtraction method, dubbed "Singular Vector Projection (SVP)" method, which exploits a priori information of the left and/or right singular vectors of the foregrounds. We demonstrate with simulation tests that this new, semi-blind method can reduce the error of the recovered 21 cm signal by orders of magnitude, even if only the left and/or right singular vectors in the largest few modes are exploited. The SVP estimators provide a new, effective approach for 21 cm observations to remove foregrounds and uncover the physics in the cosmic 21 cm signal.