21 cm Signal Recovery via Robust Principal Component Analysis

Abstract

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.

Cosmology with Phase 1 of the Square Kilometre Array Red Book 2018: Technical specifications and performance forecasts

“…In addition, Alonso et al (2015a) demonstrate how the leakage of polarised foregrounds can affect the cosmological analysis. Alternative, promising separation techniques have been proposed by Chapman et al (2013), Olivari, Remazeilles, & Dickinson (2016), Zhang et al (2016), Zuo et al (2018), which provide a diverse collection of techniques to tackle the foreground subtraction of the SKA data. Moreover, the overall effects of foreground residuals on the cosmological interpretation is dramatically reduced by combining IM data with optical galaxy surveys.…”

Prospects for measuring dark energy with 21 cm intensity mapping experiments

“…These foregrounds are orders of magnitude brighter than the cosmological signal, but fortunately, their spectral structure is basically smooth, so we can use some cleaning algorithms to remove them (e.g., Refs. [45][46][47][48][49][50][51][52][53]). In this work, we simply assume that some sort of cleaning algorithm has been applied, leaving behind some residual foreground…”

“…Fortunately, the spectral structure of the foreground sources is basically smooth, so we can use some cleaning algorithms to suppress them to a level that the cosmological H i signal can be extracted in an unbiased way (e.g., Refs. [45][46][47][48][49][50][51][52][53]). Even so, there will be some foreground contamination left.…”

An Ultra-long Wavelength Sky Model with Absorption Effect

“…These includes the Global Sky Model (GSM) (de Oliveira-Costa et al 2008), its improvements (Danny C. Price 2016;Zheng et al 2017;Sathyanarayana Rao et al 2017;Kim et al 2018), and the Self-consistent Sky Model (SSM) (Huang et al 2019). They are very useful in the design of new instruments, study of observation strategies, and testing foreground removal/mitigation methods (e.g., Shaw et al 2014;Zuo et al 2019).…”