基于鲁棒主元分析的21 cm信号恢复
21cm Signal Recovery via the Robust Principle Component Analysis
摘要：
来自中性氢（HI）的红移21~cm信号是一种潜在的强有力的宇宙学探测器，但其观测困难在于它比银河系和河外射电源的前景辐射弱得多。然而，不同频率的前景辐射沿着一条视线是相干的，并且已经提出了基于该特性的各种前景减法方法。本文提出了一种基于鲁棒主成分分析（RPCA）的21 cm信号提取方法，该方法充分利用了21 cm信号频率协方差矩阵的稀疏性和前景信号频率协方差矩阵的低秩特性（即频率相干性），从而实现了21 cm信号的提取。前景频率协方差的低秩属性已被利用在许多以前的工作前景减法，但据我们所知，21厘米信号的频率协方差的稀疏性首次探讨在这里。通过利用RPCA方法中的这两个性质，原则上，前景和信号可以在没有信号损失问题的情况下分离。我们的方法既适用于平天近似下的小块天空，也适用于必须考虑球度的大面积天空。它也很容易被扩展到处理更复杂的情况，如天空地图的缺陷。
英文摘要：
The redshifted 21~cm signal from neutral hydrogen (HI) is potentially a very powerful probe for cosmology, but a difficulty in its observation is that it is much weaker than foreground radiation from the Milky Way as well as extragalactic radio sources. The foreground radiation at different frequencies are however coherent along one line of sight, and various methods of foreground subtraction based on this property have been proposed. In this paper, we present a new method based on the Robust Principal Component Analysis (RPCA) to subtract foreground and extract 21~cm signal, which explicitly uses both the low-rank property of the frequency covariance matrix (i.e. frequency coherence) of the foreground and the sparsity of the frequency covariance matrix of the 21~cm signal. The low-rank property of the foregrounds frequency covariance has been exploited in many previous works on foreground subtraction, but to our knowledge the sparsity of the frequency covariance of the 21~cm signal is first explored here. By exploiting both properties in the RPCA method, in principle, the foreground and signal may be separated without the signal loss problem. Our method is applicable to both small patch of sky with the flat-sky approximation, and to large area of sky where the sphericity has to be considered. It is also easy to be extended to deal with more complex conditions such as sky map with defects.
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