P. Paykari

WMAP nine-year CMB estimation using sparsity

Recovering the Cosmic Microwave Background (CMB) from WMAP data requires galactic foreground emissions to be accurately separated out. Most component separation techniques rely on second order statistics such as Internal Linear Combination (ILC) techniques. In this paper, we present a new WMAP 9-year CMB map, with 15 arcmin resolution, which is reconstructed using a recently introduced sparse component separation technique, coined Local Generalized Morphological Component Analysis (LGMCA). LGMCA emphasizes on the sparsity of the components to be retrieved in the wavelet domain. We show that although 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.

PRISM: Sparse recovery of the primordial power spectrum

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 maps. Methods. A sparsity-based linear inversion method, named 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 nine-year simulated data for three types of primordial power spectra: a near scale-invariant spectrum, a spectrum with a small running of the spectral index, and a spectrum with a localised feature. This technique proves that it can 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 nine-year data and find no significant departure from a near scaleinvariant 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.

PRISM: Recovery of the primordial spectrum from Planck data

Aim. 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 algorithms ability to recover a small localised feature at k similar to 0.125 Mpc(-1), which caused a large dip at l similar to 1800 in the angular power spectrum. Conclusions. We find no significant departures from the fiducial Planck PR1 near scale-invariant primordial power spectrum with A(s) = 2.215 x 10(-9) and n(s) = 0.9624.

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

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 χ2 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.

True cosmic microwave background power spectrum estimation

Aims. The cosmic microwave background (CMB) power spectrum is a powerful cosmological probe as it entails almost the entire statistical information of CMB perturbations. Having access to only one sky, the CMB power spectrum measured by our experiments is only a realization of the true underlying angular power spectrum. We aim to recover the true underlying CMB power spectrum from the one realization that we have without knowing the cosmological parameters. Methods. The sparsity of the CMB power spectrum is rst investigated in two dictionaries; discrete cosine transform (DCT) and wavelet transform (WT). The CMB power spectrum can be recovered with very few coe cients in these two dictionaries and hence is very compressible. Results. We studied the performance of these dictionaries in smoothing a set of simulated power spectra. Based on this, we developed a technique that estimates the true underlying CMB power spectrum from data, i.e., without a need to know the cosmological parameters. Conclusions. This smooth estimated spectrum can be used to simulate CMB maps with similar properties as the true CMB simulations with the correct cosmological parameters. This allows us to perform Monte Carlo simulations in a given project without having to know the cosmological parameters. The developed IDL code, TOUSI, for theoretical power spectrum using sparse estimation, will be released with the next version of ISAP.

PRISM: Sparse recovery of the primordial spectrum from WMAP9 and Planck datasets

The primordial power spectrum is an indirect probe of inflation or other structure-formation mechanisms. We introduce a new method, named \textbf{PRISM}, to estimate this spectrum from the empirical cosmic microwave background (CMB) power spectrum. This is a sparsity-based inversion method, which leverages a sparsity prior on features in the primordial spectrum in a wavelet dictionary to regularise the inverse problem. This non-parametric approach is able to reconstruct the global shape as well as localised features of spectrum accurately and proves to be robust for detecting deviations from the currently favoured scale-invariant spectrum. We investigate the strength of this method on a set of WMAP nine-year simulated data for three types of primordial spectra and then process the WMAP nine-year data as well as the Planck PR1 data. We find no significant departures from a near scale-invariant spectrum.

Theoretical Power Spectrum Estimation from Cosmic Microwave Background Data

The cosmic microwave background (CMB) power spectrum is a powerful cosmological probe as it entails almost all the statistical information of the CMB perturbations. Having access to only one sky, the CMB spectrum measured by our experiments is only a realization of the true underlying angular power spectrum. In this paper we use the sparsity of the CMB spectrum to develop a technique that estimates the true underlying CMB power spectrum from data alone. The developed IDL code, TOUSI, for Theoretical pOwer spectrUm using Sparse estImation, will be released with the next version of ISAP.