Entropy and astronomical data analysis: Perspectives from multiresolution analysis

Starck, Jean-Luc; Murtagh, Fionn; Querre, P.; Bonnarel, F.

doi:10.1051/0004-6361:20000575

“…Full details of the minimization algorithm can be found in Starck et al (2001), in addition to a description of how to determine the regularization parameter β automatically.…”

Section: Appendix A: the Fdr Methodsmentioning

confidence: 99%

Cosmological model discrimination with weak lensing

Pires

¹

,

Starck

²

,

Amara

³

et al. 2009

A&A

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Weak gravitational lensing provides a unique way of mapping directly the dark matter in the Universe. The majority of lensing analyses use the two-point statistics of the cosmic shear field to constrain the cosmological model, a method that is affected by degeneracies, such as that between σ 8 and Ω m which are respectively the rms of the mass fluctuations on a scale of 8 Mpc/h and the matter density parameter, both at z = 0. However, the two-point statistics only measure the Gaussian properties of the field, and the weak lensing field is non-Gaussian. It has been shown that the estimation of non-Gaussian statistics for weak lensing data can improve the constraints on cosmological parameters. In this paper, we systematically compare a wide range of non-Gaussian estimators to determine which one provides tighter constraints on the cosmological parameters. These statistical methods include skewness, kurtosis, and the higher criticism test, in several sparse representations such as wavelet and curvelet; as well as the bispectrum, peak counting, and a newly introduced statistic called wavelet peak counting (WPC). Comparisons based on sparse representations indicate that the wavelet transform is the most sensitive to non-Gaussian cosmological structures. It also appears that the most helpful statistic for non-Gaussian characterization in weak lensing mass maps is the WPC. Finally, we show that the σ 8 -Ω m degeneracy could be even better broken if the WPC estimation is performed on weak lensing mass maps filtered by the wavelet method, MRLens.

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“…Full details of the minimization algorithm can be found in Starck et al (2001), as well as the way to determine automatically the regularization parameter β.…”

Section: Appendix A: the Fdr Methodsmentioning

confidence: 99%

Cosmological model discrimination from weak lensing data

Pires¹,

Starck²,

Amara³

et al. 2010

AIP Conference Proceedings

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Weak gravitational lensing provides a unique way of mapping directly the dark matter in the Universe. The majority of lensing analyses use the two-point statistics of the cosmic shear field to constrain the cosmological model, a method that is affected by degeneracies, such as that between 8 and Ωm which are respectively the rms of the mass fluctuations on a scale of 8 Mpc/h and the matter density parameter, both at z = 0. However, the two-point statistics only measure the Gaussian properties of the field, and the weak lensing field is non-Gaussian. It has been shown that the estimation of non-Gaussian statistics for weak lensing data can improve the constraints on cosmological parameters. In this paper, we systematically compare a wide range of non-Gaussian estimators to determine which one provides tighter constraints on the cosmological parameters. These statistical methods include skewness, kurtosis, and the higher criticism test, in several sparse representations such as wavelet and curvelet; as well as the bispectrum, peak counting, and a newly introduced statistic called wavelet peak counting (WPC). Comparisons based on sparse representations indicate that the wavelet transform is the most sensitive to non-Gaussian cosmological structures. It also appears that the most helpful statistic for non-Gaussian characterization in weak lensing mass maps is the WPC. Finally, we show that the 8-Ωm degeneracy could be even better broken if the WPC estimation is performed on weak lensing mass maps filtered by the wavelet method, MRLens. Abstract Weak gravitational lensing provides a unique method to map directly the dark matter in the Universe. The majority of lensing analyses uses the two-point statistics of the cosmic shear field to constrain the cosmological model yielding degeneracies, such as that between σ8 and Ωm, respectively the r.m.s. of the mass fluctuations at a scale of 8M pc/h and the matter density parameter both at z = 0. However, the two-point statistics only measure the Gaussian properties of the field and the weak lensing field is non-Gaussian. It has been shown that the estimation of non-Gaussian statistics on weak lensing data can improve the constraints on cosmological parameters. In this paper, we systematically compare a wide range of non-Gaussian estimators in order to determine which one provides tighter constraints on the cosmological parameters. These statistical methods include skewness, kurtosis and the Higher Criticism test in several sparse representations such as wavelet and curvelet; as well as the bispectrum, peak counting and a new introduced statistic called Wavelet Peak Counting (W P C). Comparisons based on sparse representations show that the wavelet transform is the most sensitive to non-Gaussian cosmological structures. It appears also that the best statistic for non-Gaussian characterization in weak lensing mass maps is the W P C. Finally, we show that the σ8-Ωm degeneracy could be even better broken if the WPC estimation is performed on weak lensing mass maps filt...

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“…The Maximum Entropy Method (MEM) is well-known and widely used in image analysis in astronomy (see Bridle et al 1998;Starck et al 2001;Marshall et al 2002;, for a full description). It considers both the data and the solution as probability density functions and finds the solution using a Bayesian approach and adding a prior (the entropy) on the solution.…”

Section: Maximum Entropy Methodsmentioning

confidence: 99%

“…More generally MEM method presents many drawbacks (Narayan & Nityananda 1986;Starck et al 2001) and various refinements of MEM have been proposed over the years (Weir 1992;Bontekoe et al 1994;Pantin & Starck 1996;Starck et al 2001). The last developments have led to the so called Multiscale Entropy (Pantin & Starck 1996;Starck et al 2001;Maisinger et al 2004) which is based on an undecimated isotropic wavelet transform (à trous algorithm) (Starck et al 1998). It has been shown that the main MEM drawbacks (model dependent solution, oversmoothing of compact objects, .…”

Section: Maximum Entropy Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Weak lensing mass reconstruction using wavelets

Starck

¹

,

Pires

²

,

Réfrégier

³

2006

A&A

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This paper presents a new method for the reconstruction of weak lensing mass maps. It uses the multiscale entropy concept, which is based on wavelets, and the False Discovery Rate (FDR) which allows us to derive robust detection levels in wavelet space. We show that this new restoration approach outperforms several standard techniques currently used for weak shear mass reconstruction. This method can also be used to separate E and B modes in the shear field, and thus test for the presence of residual systematic effects. We concentrate on large blind cosmic shear surveys, and illustrate our results using simulated shear maps derived from N-Body ΛCDM simulations (Vale & White 2003) with added noise corresponding to both ground-based and space-based observations.

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Entropy and astronomical data analysis: Perspectives from multiresolution analysis

Cited by 48 publications

References 37 publications

Cosmological model discrimination with weak lensing

Cosmological model discrimination with weak lensing

Cosmological model discrimination from weak lensing data

Weak lensing mass reconstruction using wavelets

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