CMB data analysis and sparsity

Abrial, P.; Moudden, Y.; Starck, Jean-Luc; Fadili, Jalal M.; Delabrouille, J.; Nguyen, Maï K.

doi:10.1016/j.stamet.2007.11.005

Cited by 59 publications

(67 citation statements)

References 27 publications

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“…(2) The  method consists of inpainting the Galactic mask as well as the point-source holes, using the sparse-inpainting algorithm described in Abrial et al (2007Abrial et al ( , 2008. The resulting map resembles a full-sky CMB map, and therefore has no mask mean-field contribution.…”

Section: Alternative Methodsmentioning

confidence: 99%

Planck2013 results. XVII. Gravitational lensing by large-scale structure

Ade¹,

Aghanim²,

Armitage-Caplan³

et al. 2014

A&A

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On the arcminute angular scales probed by Planck, the cosmic microwave background (CMB) anisotropies are gently perturbed by gravitational lensing. Here we present a detailed study of this effect, detecting lensing independently in the 100, 143, and 217 GHz frequency bands with an overall significance of greater than 25σ. We use the temperature-gradient correlations induced by lensing to reconstruct a (noisy) map of the CMB lensing potential, which provides an integrated measure of the mass distribution back to the CMB last-scattering surface. Our lensing potential map is significantly correlated with other tracers of mass, a fact which we demonstrate using several representative tracers of large-scale structure. We estimate the power spectrum of the lensing potential, finding generally good agreement with expectations from the best-fitting ΛCDM model for the Planck temperature power spectrum, showing that this measurement at z = 1100 correctly predicts the properties of the lower-redshift, latertime structures which source the lensing potential. When combined with the temperature power spectrum, our measurement provides degeneracybreaking power for parameter constraints; it improves CMB-alone constraints on curvature by a factor of two and also partly breaks the degeneracy between the amplitude of the primordial perturbation power spectrum and the optical depth to reionization, allowing a measurement of the optical depth to reionization which is independent of large-scale polarization data. Discarding scale information, our measurement corresponds to a 4% constraint on the amplitude of the lensing potential power spectrum, or a 2% constraint on the root-mean-squared amplitude of matter fluctuations at z ∼ 2.

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Section: Alternative Methodsmentioning

confidence: 99%

Planck2013 results. XVII. Gravitational lensing by large-scale structure

Ade¹,

Aghanim²,

Armitage-Caplan³

et al. 2014

A&A

Self Cite

295

144

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“…Sparse inpainting has been proposed for filling the gaps in CMB maps (Abrial et al 2007(Abrial et al , 2008 and for weak-lensing mass map reconstruction (Pires et al 2009(Pires et al , 2010. In Perotto et al (2010), it has been shown that the sparse inpainting method does not destroy the CMB weak-lensing signal, and is therefore an elegant way to handle the mask problem.…”

Section: Appendix A: Sparse Inpaintingmentioning

confidence: 99%

“…It has been shown in Abrial et al (2008) that this inpainting technique leads to accurate CMB recovery results. More details relative to this optimisation problem can be found in Combettes & Wajs (2005); Starck et al (2010) and theoretical justifications for CMB sparse inpainting in Rauhut & Ward (2010).…”

Section: Appendix A: Sparse Inpaintingmentioning

confidence: 99%

Measuring the integrated Sachs-Wolfe effect

Dupé

Rassat

Starck

et al. 2011

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Context. One of the main challenges of modern cosmology is to understand the nature of the mysterious dark energy that causes the cosmic acceleration. The integrated Sachs-Wolfe (ISW) effect is sensitive to dark energy, and if detected in a universe where modified gravity and curvature are excluded, presents an independent signature of dark energy. The ISW effect occurs on large scales where cosmic variance is high and where owing to the Galactic confusion we lack large amounts of data in the CMB as well as large-scale structure maps. Moreover, existing methods in the literature often make strong assumptions about the statistics of the underlying fields or estimators. Together these effects can severely limit signal extraction. Aims. We aim to define an optimal statistical method for detecting the ISW effect that can handle large areas of missing data and minimise the number of underlying assumptions made about the data and estimators. Methods. We first review current detections (and non-detections) of the ISW effect, comparing statistical subtleties between existing methods, and identifying several limitations. We propose a novel method to detect and measure the ISW signal. This method assumes only that the primordial CMB field is Gaussian. It is based on a sparse inpainting method to reconstruct missing data and uses a bootstrap technique to avoid assumptions about the statistics of the estimator. It is a complete method, which uses three complementary statistical methods. Results. We apply our method to Euclid-like simulations and show we can expect a ∼7σ model-independent detection of the ISW signal with WMAP7-like data, even when considering missing data. Other tests return ∼5σ detection levels for a Euclid-like survey. We find that detection levels are independent from whether the galaxy field is normally or lognormally distributed. We apply our method to the 2 Micron All Sky Survey (2MASS) and WMAP7 CMB data and find detections in the 1.0−1.2σ range, as expected from our simulations. As a by-product, we have also reconstructed the full-sky temperature ISW field from the 2MASS data.Conclusions. We present a novel technique based on sparse inpainting and bootstrapping, which accurately detects and reconstructs the ISW effect.

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“…Furthermore, we add spatially inhomogeneous noise, which most certainly affects the results of the algorithm. Among the inpainting algorithm implemented within the multi-resolution on the sphere (MRS) package 4 , we found that the most robust results are obtained with the spherical harmonics L 1 norm minimization using wavelet packet variance regularization (Abrial et al 2007(Abrial et al , 2008.…”

Section: Update On the Fs-inpainting Methodsmentioning

confidence: 99%

A hybrid approach to cosmic microwave background lensing reconstruction from all-sky intensity maps

Plaszczynski¹,

Lavabre²,

Perotto³

et al. 2012

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On the basis of realistic simulations, we propose a hybrid method to reconstruct the lensing potential power spectrum, directly on Planck-like cosmic microwave background frequency maps. This involves the use of a large Galactic mask and the treatment of strong inhomogeneous noise. For 100, we show that a full-sky inpainting method, which was previously described, still allows a minimal variance reconstruction, with a bias that must be accounted for by a Monte Carlo method but that does not couple to the deflection field. For 100, we develop a method based on tiling the cut-sky with local 10 • × 10 • overlapping tangent planes (referred to in the following as patches). We tackle various issues related to their size/position, non-periodic boundaries, and irregularly sampled data of the planes after the sphere-to-plane projection. We show that the predominant noise term of the quadratic lensing estimator determined from an apodized patch can still be recovered directly from the data. To prevent any loss of spatial accuracy, we developed a tool that allows the efficient determination of the complex Fourier series coefficients from a bi-dimensional irregularly sampled dataset, without performing any interpolation. We show that our multi-patch approach enables the lensing power spectrum to be reconstructed with a very small bias, thanks to the omission of a Galactic mask and smaller noise inhomogeneities, as well as an almost minimal variance. At each stage, the data quality can be assessed and simple bi-dimensional spectra compiled, which allows the control of local systematic errors.

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CMB data analysis and sparsity

Cited by 59 publications

References 27 publications

Planck2013 results. XVII. Gravitational lensing by large-scale structure

Planck2013 results. XVII. Gravitational lensing by large-scale structure

Measuring the integrated Sachs-Wolfe effect

A hybrid approach to cosmic microwave background lensing reconstruction from all-sky intensity maps

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