Foreground Mitigation and Power Spectrum Analysis for Tianlai Full-sky 21 cm Survey Observation

Abstract We present a comprehensive analysis of the 21 cm intensity mapping (IM) data from the Tianlai Cylinder Pathfinder Array, focusing on multi-scale foreground mitigation and three-dimensional power spectrum estimation. Utilizing 20 days of drift-scan observations (714.4–781.7 MHz, corresponding to H i emission at redshift z  ≈ 0.82–0.99), we reconstruct high-fidelity sky maps by incorporating a high-precision, drone-measured primary beam model. This in-situ calibration significantly enhances reconstruction accuracy over previous analytical approximations. To address astrophysical foregrounds, which exceed the cosmological signal by approximately five orders of magnitude, we implement a robust multi-scale subtraction strategy—mPCA-UWTS—which combines an isotropic Undecimated Wavelet Transform on the Sphere with independent Principal Component Analysis within each wavelet domain. We subsequently estimate the 3D power spectrum via Spherical Fourier–Bessel (SFB) decomposition, providing a mathematically rigorous treatment of wide-angle and line-of-sight curvature effects inherent in wide-field surveys. Our analysis demonstrates that the SFB framework effectively isolates systematic contaminants and recovers the clustering signal without the biases introduced by conventional flat-sky approximations. This work represents the first application of the SFB formalism to observational 21 cm IM data, establishing it as a computationally efficient and scalable diagnostic tool for the next generation of wide-field 21 cm surveys, including the Square Kilometre Array and the full Tianlai array.