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Register a new userA Novel CMB Component Separation Method: Hierarchical Generalized Morphological Component Analysis
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Sebastian Wagner-Carena
Publication date
2019
fields
Physics
and research's language is
English
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We present a novel technique for Cosmic Microwave Background (CMB) foreground subtraction based on the framework of blind source separation. Inspired by previous work incorporating local variation to Generalized Morphological Component Analysis (GMCA), we introduce Hierarchical GMCA (HGMCA), a Bayesian hierarchical graphical model for source separation. We test our method on $N_{rm side}=256$ simulated sky maps that include dust, synchrotron, free-free and anomalous microwave emission, and show that HGMCA reduces foreground contamination by $25%$ over GMCA in both the regions included and excluded by the Planck UT78 mask, decreases the error in the measurement of the CMB temperature power spectrum to the $0.02-0.03%$ level at $ell>200$ (and $<0.26%$ for all $ell$), and reduces correlation to all the foregrounds. We find equivalent or improved performance when compared to state-of-the-art Internal Linear Combination (ILC)-type algorithms on these simulations, suggesting that HGMCA may be a competitive alternative to foreground separation techniques previously applied to observed CMB data. Additionally, we show that our performance does not suffer when we perturb model parameters or alter the CMB realization, which suggests that our algorithm generalizes well beyond our simplified simulations. Our results open a new avenue for constructing CMB maps through Bayesian hierarchical analysis.
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Key to any cosmic microwave background (CMB) analysis is the separation of the CMB from foreground contaminants. In this paper we present a novel implementation of Bayesian CMB component separation. We sample from the full posterior distribution using the No-U-Turn Sampler (NUTS), a gradient based sampling algorithm. Alongside this, we introduce new foreground modelling approaches. We use the mean-shift algorithm to define regions on the sky, clustering according to naively estimated foreground spectral parameters. Over these regions we adopt a complete pooling model, where we assume constant spectral parameters, and a hierarchical model, where we model individual spectral parameters as being drawn from underlying hyper-distributions. We validate the algorithm against simulations of the LiteBIRD and C-BASS experiments, with an input tensor-to-scalar ratio of $r=5times 10^{-3}$. Considering multipoles $32leqellleq 121$, we are able to recover estimates for $r$. With LiteBIRD only observations, and using the complete pooling model, we recover $r=(10pm 0.6)times 10^{-3}$. For C-BASS and LiteBIRD observations we find $r=(7.0pm 0.6)times 10^{-3}$ using the complete pooling model, and $r=(5.0pm 0.4)times 10^{-3}$ using the hierarchical model. By adopting the hierarchical model we are able to eliminate biases in our cosmological parameter estimation, and obtain lower uncertainties due to the smaller Galactic emission mask that can be adopted for power spectrum estimation. Measured by the rate of effective sample generation, NUTS offers performance improvements of $sim10^3$ over using Metropolis-Hastings to fit the complete pooling model. The efficiency of NUTS allows us to fit the more sophisticated hierarchical foreground model, that would likely be intractable with non-gradient based sampling algorithms.
The polarization modes of the cosmological microwave background are an invaluable source of information for cosmology, and a unique window to probe the energy scale of inflation. Extracting such information from microwave surveys requires disentangling between foreground emissions and the cosmological signal, which boils down to solving a component separation problem. Component separation techniques have been widely studied for the recovery of CMB temperature anisotropies but quite rarely for the polarization modes. In this case, most component separation techniques make use of second-order statistics to discriminate between the various components. More recent methods, which rather emphasize on the sparsity of the components in the wavelet domain, have been shown to provide low-foreground, full-sky estimate of the CMB temperature anisotropies. Building on sparsity, the present paper introduces a new component separation technique dubbed PolGMCA (Polarized Generalized Morphological Component Analysis), which refines previous work to specifically tackle the estimation of the polarized CMB maps: i) it benefits from a recently introduced sparsity-based mechanism to cope with partially correlated components, ii) it builds upon estimator aggregation techniques to further yield a better noise contamination/non-Gaussian foreground residual trade-off. The PolGMCA algorithm is evaluated on simulations of full-sky polarized microwave sky simulations using the Planck Sky Model (PSM), which show that the proposed method achieve a precise recovery of the CMB map in polarization with low noise/foreground contamination residuals. It provides improvements with respect to standard methods, especially on the galactic center where estimating the CMB is challenging.
Foreground components in the Cosmic Microwave Background (CMB) are sparse in a needlet representation, due to their specific morphological features (anisotropy, non-Gaussianity). This leads to the possibility of applying needlet thresholding procedures as a component separation tool. In this work, we develop algorithms based on different needlet-thresholding schemes and use them as extensions of existing, well-known component separation techniques, namely ILC and template-fitting. We test soft- and hard-thresholding schemes, using different procedures to set the optimal threshold level. We find that thresholding can be useful as a denoising tool for internal templates in experiments with few frequency channels, in conditions of low signal-to-noise. We also compare our method with other denoising techniques, showing that thresholding achieves the best performance in terms of reconstruction accuracy and data compression while preserving the map resolution. The best results in our tests are in particular obtained when considering template-fitting in an LSPE like experiment, especially for B-mode spectra.
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Observing the neutral Hydrogen (HI) distribution across the Universe via redshifted 21-cm line Intensity Mapping (IM) constitutes a powerful probe for cosmology. However, this redshifted 21cm signal is obscured by the foreground emission. This paper addresses the capabilities of the BINGO survey to separate such signals. Specifically, this paper (a) looks in detail at the different residuals left over by foreground components, (b) shows that a noise-corrected spectrum is unbiased and (c) shows that we understand the remaining systematic residuals by analyzing non-zero contributions to the three point function. We use the Generalized Needlet Internal Linear Combination (GNILC), which we apply to sky simulations of the BINGO experiment for each redshift bin of the survey. We present our recovery of the redshifted 21-cm signal from sky simulations of the BINGO experiment including foreground components. We test the recovery of the 21-cm signal through the angular power spectrum at different redshifts, as well as the recovery of its non-Gaussian distribution through a bispectrum analysis. We find that non-Gaussianities from the original foreground maps can be removed down to, at least, the noise limit of the BINGO survey with such techniques. Our bispectrum analysis yields strong tests of the level of the residual foreground contamination in the recovered 21-cm signal, thereby allowing us to both optimize and validate our component separation analysis. (Abridged)
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