Sparse estimation of model-based diffuse thermal dust emission

 

Authors: M.O. Irfan, J.Bobin 
Journal: MNRAS
Year: 2017
Download: ADS | arXiv


Abstract

Component separation for the Planck HFI data is primarily concerned with the estimation of thermal dust emission, which requires the separation of thermal dust from the cosmic infrared background (CIB). For that purpose, current estimation methods rely on filtering techniques to decouple thermal dust emission from CIB anisotropies, which tend to yield a smooth, low- resolution, estimation of the dust emission. In this paper we present a new parameter estimation method, premise: Parameter Recovery Exploiting Model Informed Sparse Estimates. This method exploits the sparse nature of thermal dust emission to calculate all-sky maps of thermal dust temperature, spectral index and optical depth at 353 GHz. premise is evaluated and validated on full-sky simulated data. We find the percentage difference between the premise results and the true values to be 2.8, 5.7 and 7.2 per cent at the 1 sigma level across the full sky for thermal dust temperature, spectral index and optical depth at 353 GHz, respectively. Comparison between premise and a GNILC-like method over selected regions of our sky simulation reveals that both methods perform comparably within high signal-to-noise regions. However outside of the Galactic plane premise is seen to outperform the GNILC-like method with increasing success as the signal-to-noise ratio worsens.

CMB reconstruction from the WMAP and Planck PR2 data

 

Authors:  J. Bobin, F. Sureau and J. -L. Starck
Journal: A&A
Year: 2015
Download: ADS | arXiv


Abstract

In this article, 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 WMAP nine-years. It provides more than a mere update of the CMB map introduced in (Bobin et al. 2014b) since it benefits from an improvement of the component separation method L-GMCA (Local-Generalized Morphological Component Analysis) that allows the efficient separation of correlated components (Bobin et al. 2015). Based on the most recent CMB data, we further confirm previous results (Bobin et al. 2014b) showing that the proposed CMB map estimate exhibits appealing characteristics for astrophysical and cosmological applications: i) it is a full sky map that did not require any inpainting or interpolation post-processing, ii) foreground contamination is showed to be very low even on the galactic center, iii) it does not exhibit any detectable trace of thermal SZ 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.

PRISM: Recovery of the primordial spectrum from Planck data

 

Authors:  F. Lanusse, P. Paykari, J. -L. Starck et al.
Journal: A&A
Year: 2014
Download: ADS | arXiv


Abstract

Aims. The primordial power spectrum describes the initial perturbations that seeded the large-scale structure we observe today. It provides an indirect probe of inflation or other structure-formation mechanisms. In this letter, we recover the primordial power spectrum from the Planck PR1 dataset, using our recently published algorithm PRISM.
Methods. PRISM is a sparsity-based inversion method, that aims at recovering features in the primordial power spectrum from the empirical power spectrum of the cosmic microwave background (CMB). This ill-posed inverse problem is regularised using a sparsity prior on features in the primordial power spectrum in a wavelet dictionary. Although this non-parametric method does not assume a strong prior on the shape of the primordial power spectrum, it is able to recover both its general shape and localised features. As a results, this approach presents a reliable way of detecting deviations from the currently favoured scale-invariant spectrum.
Results. We applied PRISM to 100 simulated Planck data to investigate its performance on Planck-like data. We then applied PRISM to the Planck PR1 power spectrum to recover the primordial power spectrum. We also tested the algorithm’s ability to recover a small localised feature at k ∼ 0.125 Mpc−1, which caused a large dip at l ∼ 1800 in the angular power spectrum.
Conclusions. We find no significant departures from the fiducial Planck PR1 near scale-invariant primordial power spectrum with As = 2.215 × 10−9 and ns = 0.9624.

Sparse point-source removal for full-sky CMB experiments: application to WMAP 9-year data

 

Authors:  F. C. Sureau, J. -L. Starck, J. Bobin et al. 
Journal: A&A
Year: 2014
Download: ADS | arXiv


Abstract

Missions such as WMAP or Planck measure full-sky fluctuations of the cosmic microwave background and foregrounds, among which bright compact source emissions cover a significant fraction of the sky. To accurately estimate the diffuse components, the point-source emissions need to be separated from the data, which requires a dedicated processing. We propose a new technique to estimate the flux of the brightest point sources using a morphological separation approach: point sources with known support and shape are separated from diffuse emissions that are assumed to be sparse in the spherical harmonic domain. This approach is compared on both WMAP simulations and data with the standard local chi2 minimization, modelling the background as a low-order polynomial. The proposed approach generally leads to 1) lower biases in flux recovery, 2) an improved root mean-square error of up to 35% and 3) more robustness to background fluctuations at the scale of the source. The WMAP 9-year point-source-subtracted maps are available online.

Planck CMB Anomalies: Astrophysical and Cosmological Secondary Effects and the Curse of Masking

 

Authors:  A. Rassat, J. -L. Starck , P. Paykari et al.
Journal: JCAP
Year: 2014
Download: ADS | arXiv


Abstract

Large-scale anomalies have been reported in CMB data with both WMAP and Planck data. These could be due to foreground residuals and or systematic effects, though their confirmation with Planck data suggests they are not due to a problem in the WMAP or Planck pipelines. If these anomalies are in fact primordial, then understanding their origin is fundamental to either validate the standard model of cosmology or to explore new physics. We investigate three other possible issues: 1) the trade-off between minimising systematics due to foreground contamination (with a conservative mask) and minimising systematics due to masking, 2) astrophysical secondary effects (the kinetic Doppler quadrupole and kinetic Sunyaev-Zel'dovich effect), and 3) secondary cosmological signals (the integrated Sachs-Wolfe effect). We address the masking issue by considering new procedures that use both WMAP and Planck to produce higher quality full-sky maps using the sparsity methodology (LGMCA maps). We show the impact of masking is dominant over that of residual foregrounds, and the LGMCA full-sky maps can be used without further processing to study anomalies. We consider four official Planck PR1 and two LGMCA CMB maps. Analysis of the observed CMB maps shows that only the low quadrupole and quadrupole-octopole alignment seem significant, but that the planar octopole, Axis of Evil, mirror parity and cold spot are not significant in nearly all maps considered. After subtraction of astrophysical and cosmological secondary effects, only the low quadrupole may still be considered anomalous, meaning the significance of only one anomaly is affected by secondary effect subtraction out of six anomalies considered.

PRISM: Sparse Recovery of the Primordial Power Spectrum

 

Authors: P. Paykari, F. Lanusse, J. -L. Starck et al.
Journal: A&A
Year: 2014
Download: ADS | arXiv


Abstract

Aims. The primordial power spectrum describes the initial perturbations in the Universe which eventually grew into the large-scale structure we observe today, and thereby provides an indirect probe of inflation or other structure-formation mechanisms. Here, we introduce a new method to estimate this spectrum from the empirical power spectrum of cosmic microwave background (CMB) maps.
Methods. A sparsity-based linear inversion method, coined PRISM, is presented. This technique leverages a sparsity prior on features in the primordial power spectrum in a wavelet basis to regularise the inverse problem. This non- parametric approach does not assume a strong prior on the shape of the primordial power spectrum, yet is able to correctly reconstruct its global shape as well as localised features. These advantages make this method robust for detecting deviations from the currently favoured scale-invariant spectrum.
Results. We investigate the strength of this method on a set of WMAP 9-year simulated data for three types of primordial power spectra: a nearly scale-invariant spectrum, a spectrum with a small running of the spectral index, and a spectrum with a localised feature. This technique proves to easily detect deviations from a pure scale-invariant power spectrum and is suitable for distinguishing between simple models of the inflation. We process the WMAP 9-year data and find no significant departure from a nearly scale-invariant power spectrum with the spectral index ns = 0.972. Conclusions. A high resolution primordial power spectrum can be reconstructed with this technique, where any strong local deviations or small global deviations from a pure scale-invariant spectrum can easily be detected.


Summary

The primordial power spectrum describes the initial perturbations in the Universe which eventually grew into the large-scale structure we observe today, and thereby provides an indirect probe of inflation or other structure-formation mechanisms. The primordial power spectrum is therefore linked to cosmological observables and in particular the Cosmic Microwave Background (CMB). However, due to degeneracies in the transfer function that links the primordial power spectrum to the measured CMB, recovering the primordial power spectrum constitutes a non-trivial ill-posed inverse problem. Furthermore, the multiplicative nature of the noise on the estimator of CMB power spectrum adds to the complexity of the problem. PRISM is a new sparsity-based, non-linear reconstruction technique which aims at reconstructing global and local features on the primordial power spectrum from CMB measurements. Features are detected and reconstructed based on their significance compared to noise. The PRISM software is part of the ISAP package and will be included in the next release of the package. The figure below shows reconstructions of a primordial power spectrum with a localized feature around 0.03 Mpc using PRISM.


The algorithm

The primordial power spectrum reconstruction problem is an ill-posed linear inverse problem which we address through the framework of sparse regularisation. This framework allows for accurate and robust recovery by leveraging a sparsity prior on the signal to recover (i.e. it is assumed that it can be represented using a small number of coefficients in an adapted dictionary). Formally, the observed pseudo-power spectrum \widetilde{C}_\ell computed from masked CMB maps can be linked to the underlying primordial power spectrum P_k through a linear relation of the form:

\widetilde{C}_\ell = \left( \mathbf{M} P_k \right) Z_\ell

where \mathbf{M} is a linear operator that encodes the angular transfer function of CMB anisotropies and the effects of masks and beams, and \mathbf{Z_\ell} is a multipicative noise term. The recovery of the primordial power spectrum is performed by solving an optimization problem of the form:

\min\limits_{X} \quad \frac{1}{2} \underbrace{\parallel C_\ell - \mathbf{M} X \parallel^{2}_{2}}_{\mbox{data fidelity term}} \quad + \quad \lambda \underbrace{\parallel \mathbf{\Phi} X \parallel_{1}}_{\mbox{sparsity promoting term}}

where \mathbf{\Phi} is a wavelet transform. To estimate the unknown quantity C_\ell - \mathbf{M} X from the noisy quantity \widetilde{C}_\ell - \mathbf{M} X, we use a variance stabilisation approach derived from the technique used in the TOUSI algorithm (Paykari et al. (2012)) and based on the Whaba variance stabilisation transform.


Results on simulations

To assess the performance of PRISM we produced a large number of Monte-Carlo CMB simulations for different test power spectra. We tested a near scale invariant primordial power spectra with ns=0.972, a power spectrum with a running of the spectral index with ns=0.972, \alpha_s= -0.017 (see figure below), and a power law spectrum with a localised feature around 0.3 Mpc (see above figure).

Joint Planck and WMAP CMB Map Reconstruction

 

Authors: J. Bobin,  F. Sureau, J. -L. Starck et al.
Journal: A&A
Year: 2014
Download: ADS | arXiv


Abstract

We present a novel estimate of the cosmological microwave background (CMB) map by combining the two latest full-sky microwave surveys: WMAP nine-year and Planck PR1. The joint processing benefits from a recently introduced component separation method coined "local-generalized morphological component analysis'' (LGMCA) based on the sparse distribution of the foregrounds in the wavelet domain. The proposed estimation procedure takes advantage of the IRIS 100 micron as an extra observation on the galactic center for enhanced dust removal. We show that this new CMB map presents several interesting aspects: i) it is a full sky map without using any inpainting or interpolating method, ii) foreground contamination is very low, iii) the Galactic center is very clean, with especially low dust contamination as measured by the cross-correlation between the estimated CMB map and the IRIS 100 micron map, and iv) it is free of thermal SZ contamination.


Summary

The LGMCA method has been used to reconstruct the Cosmic Microwave Background (CMB) image from WMAP 9 year and Planck-PR1 data. Based on the sparse modeling of signals - a framework recently developed in applied mathematics - the proposed component separation method is well-suited for the extraction of foreground emissions. A joint WMAP9 year and Planck PR1 CMB has been reconstructed for the first time and produce a very high quality CMB map, especially on the galactic center where it is the most difficult due to the strong foreground emissions of our Galaxy. We compare the LGMCA results with other CMB Planck PR1 maps:

Comparison on the Galactic centre centered at (l,b)=(37.7,0). Top, PR1 NILC and SEVEM CMB maps, and bottom, PR1 SMICA and WPR1 LGMCA CMB maps:

Quality maps:

It is usually hard to derive a discriminative criterion from real data. For that purpose, the quality map measures an excess of power in the estimated CMB map in the wavelet domain with the respect to the expected power of the CMB. The expected CMB power is computed from the Planck best-fit power spectrum assuming a fiducial cosmology.

The LGMCA CMB map does not contain noticeable tSZ residuals (coma cluster area):

The maps below shows the differences between HFI-217GHz and CMB maps, respectively PR1 NILC, SEVEM, SMICA and WPR1 LGMCA. As the SZ vanishes at 217GHz, the presence of residuals of tSZ in the difference reveals a tSZ contamination in the estimated CMB map.

Below we show the power spectra.  Left, estimated power spectrum of the WPR1 LGMCA map (red) and official PR1 power spectrum (green). The solid black line is the Planck-only best-fit Cl provided by the Planck consortium. Right, power spectrum in logarithmic scale. Error bars are set to 1 sigma.

And finally, the difference spectra. Left, difference between the power spectrum estimated from the WPR1 LGMCA map (red) (resp. official PR1 power spectrum (green)) and the Planck-only best-fit provided by the Planck consortium. Right, difference between the estimated and theoretical power spectra in logarithmic scale. Error bars are set to 1 sigma.

This clean and truly full-sky estimate of the CMB map is a very good candidate for galactic studies. Being free of noticeable remainings of thermal SZ, it will be helpful for kinetic SZ studies. As well, following the philosophy of reproducible research, the LCS makes available all the codes used to estimate and evaluate the CMB map.

Removal of two large-scale cosmic microwave background anomalies after subtraction of the integrated Sachs-Wolfe effect

 

Authors: A. Rassat, J. -L. Starck and F. -X. Dupe
Journal: A&A
Year: 2013
Download: ADS | arXiv


Abstract

Though debated, the existence of claimed large-scale anomalies in the CMB is not totally dismissed. In parallel to the debate over their statistical significance, recent work focussed on masks and secondary anisotropies as potential sources of these anomalies. In this work we investigate simultaneously the impact of the method used to account for masked regions and the impact of the ISW effect, which is the large-scale secondary anisotropy most likely to affect the CMB anomalies. In this sense, our work is an update of both Francis & Peacock 2010 and Kim et al. 2012. Our aim is to identify trends in CMB data with different mask treatments. We reconstruct the ISW signal due to 2MASS and NVSS galaxies. We account for missing data using the sparse inpainting technique of Abrial et al. 2008 and sparse inpainting of the CMB, LSS and ISW and find that it constitutes a bias-free reconstruction method suitable to study large-scale statistical isotropy and the ISW effect. We focus on three large-scale CMB anomalies: the low quadrupole, the quad/oct alignment, and the octopole planarity. After sparse inpainting, the low quadrupole becomes more anomalous, whilst the quad/oct alignment becomes less anomalous. The significance of the low quadrupole is unchanged after subtraction of the ISW effect, while the trend is that the quad/oct alignment has reduced significance, yet other hypotheses remain possible as well (e.g. exotic physics). Our results also suggest that both of these anomalies may be due to the quadrupole alone. The octopole planarity significance is also reduced after inpainting and after ISW subtraction, however, we do not find that it was very anomalous to start with.

WMAP 9-year CMB estimation using sparsity

 

Authors:  J. Bobin, F. Sureau , P. Paykari et al.
Journal: A&A
Year: 2013
Download: ADS | arXiv


Abstract

Recovering the cosmic microwave background (CMB) from WMAP data requires that Galactic foreground emissions are accurately separated out. Most component separation techniques rely on second-order statistics such as internal linear combination (ILC) techniques. We present a new WMAP nine-year CMB map with a resolution of 15 arcmin, which is reconstructed using a recently introduced sparse-component separation technique, called local generalized morphological component analysis (LGMCA). This focuses on the sparsity of the components to be retrieved in the wavelet domain. We show that although they are derived from a radically different separation criterion (i.e. sparsity), the LGMCA-WMAP 9 map and its power spectrum are fully consistent with their more recent estimates from WMAP 9.

On Preferred Axes in WMAP Cosmic Microwave Background Data after Subtraction of the Integrated Sachs-Wolfe Effect

 

Authors:  A. Rassat and J. -L. Starck 
Journal: A&A
Year: 2013
Download: ADS | arXiv


Abstract

There is currently a debate over the existence of claimed statistical anomalies in the cosmic microwave background (CMB), recently confirmed in Planck data. Recent work has focussed on methods for measuring statistical significance, on masks and on secondary anisotropies as potential causes of the anomalies. We investigate simultaneously the method for accounting for masked regions and the foreground integrated Sachs-Wolfe (ISW) signal. We search for trends in different years of WMAP CMB data with different mask treatments. We reconstruct the ISW field due to the 2 Micron All-Sky Survey (2MASS) and the NRAO VLA Sky Survey (NVSS) up to l=5, and we focus on the Axis of Evil (AoE) statistic and even/odd mirror parity, both of which search for preferred axes in the Universe. We find that removing the ISW reduces the significance of these anomalies in WMAP data, though this does not exclude the possibility of exotic physics.