Bayes-SCF: A Bayesian filter to mitigate foreground leakage in the 21-cm power spectrum

Abstract

Missing channels in radio-interferometric visibility data can introduce systematic artefacts into the estimated 21-cm power spectrum. A common workaround is to first estimate the two-frequency correlation $C(\Delta \nu )$ and then Fourier-transform it to obtain the power spectrum $P(k_{\parallel })$. This procedure yields an unbiased estimate when the signal is statistically homogeneous (ergodic) along the line-of-sight, but it fails in the presence of non-ergodic foregrounds. Smooth Component Filtering (SCF) has recently been proposed as a solution to this problem, in which the dominant non-ergodic (spectrally smooth) component is removed prior to estimating $C(\Delta \nu )$. In existing implementations, the smooth component is estimated by convolving the visibilities with a Hann window along the frequency axis. We demonstrate that this Hann-based SCF performs adequately only when foregrounds are extremely spectrally smooth. It breaks down with increased flagging and when foregrounds exhibit spectral structures. We introduce a Bayesian extension, Bayes-SCF, based on Gaussian Process regression, which overcomes these limitations. Bayes-SCF models the smooth component via a covariance function with a fixed correlation length, enabling controlled and data-driven filtering. Using simulated data, we show that Bayes-SCF robustly recovers the input model 21-cm power spectrum in the presence of spectrally unsmooth foregrounds. The filter is demonstrated to work under different flagging patterns, including $80\%$ channels being randomly flagged. Bayes-SCF is also effective in a delay-spectrum approach. The primary trade-off introduced by the Bayesian framework is the increased computational cost; future work will focus on optimizing the algorithm and applying it to real Murchison Widefield Array data.

arXiv commentAccepted for publication in MNRAS. 22 pages, 25 figures, including appendices. The Bayes-SCF code is available at https://github.com/aecosmo/Bayes-SCF

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