A Novel CMB Component Separation Method: Hierarchical Generalized Morphological Component Analysis

TL;DR

This paper introduces Hierarchical GMCA, a Bayesian source separation method that improves CMB foreground removal, reduces contamination, and enhances the accuracy of CMB power spectrum measurements compared to existing techniques.

Contribution

The paper presents a novel hierarchical Bayesian GMCA approach for CMB foreground separation, demonstrating improved performance and robustness over traditional methods.

Findings

Reduces foreground contamination by 25% compared to GMCA.

Decreases error in CMB power spectrum measurement to 0.02-0.03%.

Performs comparably or better than state-of-the-art ILC algorithms.

Abstract

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.