Sparse blind source separation for partially correlated sources

Bobin, J.; Starck, Jean-Luc; Rapin, Jérémy; Larue, Anthony

doi:10.1109/icip.2014.7026215

Cited by 2 publications

(4 citation statements)

References 13 publications

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“…Subsequently, even theoretically decorrelated components exhibit some correlation, customarily named chance correlations, which can be regarded as partial correlation between the components. However, it has been well established that partial correlations dramatically hamper the efficiency of component separation methods (Bobin et al 2014a(Bobin et al , 2015.…”

Section: Sparse Component Separation For Cmb Reconstructionmentioning

confidence: 99%

Cosmic microwave background reconstruction from WMAP andPlanckPR2 data

Bobin

Sureau

Starck

2016

A&A

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We describe a new estimate of the cosmic microwave background (CMB) intensity map reconstructed by a joint analysis of the full Planck 2015 data (PR2) and nine years of WMAP data. The proposed map provides more than a mere update of the CMB map introduced in a previous paper since it benefits from an improvement of the component separation method L-GMCA (Local-Generalized Morphological Component Analysis), which facilitates efficient separation of correlated components. Based on the most recent CMB data, we further confirm previous results showing that the proposed CMB map estimate exhibits appealing characteristics for astrophysical and cosmological applications: i) it is a full-sky map as it did not require any inpainting or interpolation postprocessing; ii) foreground contamination is very low even on the galactic center; and iii) the map does not exhibit any detectable trace of thermal Sunyaev-Zel'dovich contamination. We show that its power spectrum is in good agreement with the Planck PR2 official theoretical best-fit power spectrum. Finally, following the principle of reproducible research, we provide the codes to reproduce the L-GMCA, which makes it the only reproducible CMB map.

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Section: Sparse Component Separation For Cmb Reconstructionmentioning

confidence: 99%

Cosmic microwave background reconstruction from WMAP andPlanckPR2 data

Bobin

Sureau

Starck

2016

A&A

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“…This algorithm has been shown to be very effective in distinguishing partially correlated sources. For more details, we refer to Bobin et al (2014a).…”

Section: Sparse Reconstruction Of the Cmb Polarization Mapsmentioning

confidence: 99%

“…The rationale of this algorithm relies on a weighting scheme that aims at penalizing correlated entries, which are the most detrimental for separation. This algorithm first means that some diagonal weight matrix Q (Bobin et al 2014a) needs to be defined, and secondly that the minimization problem in Eq. (15) needs to be substituted by Bobin et al (2014a) have shown that partially correlated samples are related to non-sparse columns of the source matrix S. Based on this relationship, it adaptively updates the weight matrix with respect to the estimated sources during the iterations of the algorithm.…”

Section: Sparse Reconstruction Of the Cmb Polarization Mapsmentioning

confidence: 99%

“…An extension of the GMCA algorithm (Bobin et al 2014a) has recently been introduced in the signal-processing community to specifically solve the separation of partially correlated sources. Its main assumption is that partial correlation between components will mainly impact a subset of the sparse decomposition coefficients.…”

Section: Sparse Reconstruction Of the Cmb Polarization Mapsmentioning

confidence: 99%

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Polarized cosmic microwave background map recovery with sparse component separation

Bobin

Sureau

Starck

2015

A&A

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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 this information from microwave surveys requires distinguishing between foreground emissions and the cosmological signal, which means solving a component separation problem. Component separation techniques have been widely studied for the recovery of cosmic microwave background (CMB) temperature anisotropies, but very rarely for the polarization modes. In this case, most component separation techniques make use of second-order statistics to distinguish between the various components. More recent methods, which instead emphasize the sparsity of the components in the wavelet domain, have been shown to provide low-foreground, full-sky estimates of the CMB temperature anisotropies. Building on sparsity, we here introduce a new component separation technique dubbed the polarized generalized morphological component analysis (PolGMCA), which refines previous work to specifically work on 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). The simulations show that the proposed method achieves a precise recovery of the CMB map in polarization with low-noise and foreground contamination residuals. It provides improvements over standard methods, especially on the Galactic center, where estimating the CMB is challenging.

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Sparse blind source separation for partially correlated sources

Cited by 2 publications

References 13 publications

Cosmic microwave background reconstruction from WMAP andPlanckPR2 data

Cosmic microwave background reconstruction from WMAP andPlanckPR2 data

Polarized cosmic microwave background map recovery with sparse component separation

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