Localized Tight Frames on Spheres

Narcowich, Francis J.; Petrushev, Pencho; Ward, Joseph D.

doi:10.1137/040614359

Cited by 283 publications

(443 citation statements)

References 22 publications

(34 reference statements)

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“…1992). Needlets were introduced as a particular construction of a wavelet family on the sphere by Narcowich et al (2006) and Guilloux et al (2009). Needlets can be interpreted as a set of band-pass filters in harmonic space.…”

Section: Discussionmentioning

confidence: 99%

Extracting H i cosmological signal with generalized needlet internal linear combination

Olivari¹,

Remazeilles²,

Dickinson³

2015

Mon. Not. R. Astron. Soc.

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HI intensity mapping is a new observational technique to map fluctuations in the large-scale structure of matter using the 21 cm emission line of atomic hydrogen (HI). Sensitive HI intensity mapping experiments have the potential to detect Baryon Acoustic Oscillations (BAO) at low redshifts (z 1) in order to constrain the properties of dark energy. Observations of the HI signal will be contaminated by instrumental noise and, more significantly, by astrophysical foregrounds, such as Galactic synchrotron emission, which is at least four orders of magnitude brighter than the HI signal. Foreground cleaning is recognised as one of the key challenges for future radio astronomy surveys. We study the ability of the Generalized Needlet Internal Linear Combination (GNILC) method to subtract radio foregrounds and to recover the cosmological HI signal for a general HI intensity mapping experiment. The GNILC method is a new technique that uses both frequency and spatial information to separate the components of the observed data. Our results show that the method is robust to the complexity of the foregrounds. For simulated radio observations including HI emission, Galactic synchrotron, Galactic free-free, radio sources and 0.05 mK thermal noise, we find that the GNILC method can reconstruct the HI power spectrum for multipoles 30 < < 150 with 6% accuracy on 50% of the sky for a redshift z ∼ 0.25.

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Section: Discussionmentioning

confidence: 99%

Extracting H i cosmological signal with generalized needlet internal linear combination

Olivari¹,

Remazeilles²,

Dickinson³

2015

Mon. Not. R. Astron. Soc.

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“…uous representations and fast implementations that have been made available publicly, including needlets (Narcowich et al 2006;Baldi et al 2009;Marinucci et al 2008), directional scale-discretised wavelets (Wiaux et al 2008;Leistedt et al 2013;, and the isotropic undecimated and pyramidal wavelet transforms (Starck et al 2006). Each approach has also been extended to analyse spin functions on the sphere (Geller et al 2008;Geller & Marinucci 2010Geller et al 2009;McEwen et al 2015bMcEwen et al , 2014Starck et al 2009) and functions defined on the threedimensional ball formed by augmenting the sphere with the radial line (Durastanti et al 2014;Leistedt & McEwen 2012;Leistedt et al 2015;Lanusse et al 2012).…”

Section: Scale-discretised Wavelets On the Spherementioning

confidence: 99%

“…In this work we adopt directional scale-discretised wavelets (Wiaux et al 2008;Leistedt et al 2013;McEwen et al , 2015bMcEwen et al , 2016, which are essentially the generalisation of needlets (Narcowich et al 2006;Baldi et al 2009;Marinucci et al 2008) to directional wavelets . Directional scalediscretised wavelets have recently been shown to satisfy quasiexponential localisation and asymptotic uncorrelation properties similar to needlets ) and consequently have excellent spatial localisation properties.…”

Section: Scale-discretised Wavelets On the Spherementioning

confidence: 99%

Wavelet-Bayesian inference of cosmic strings embedded in the cosmic microwave background

McEwen

Feeney

Peiris

et al. 2017

Monthly Notices of the Royal Astronomical Society

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Cosmic strings are a well-motivated extension to the standard cosmological model and could induce a subdominant component in the anisotropies of the cosmic microwave background (CMB), in addition to the standard inflationary component. The detection of strings, while observationally challenging, would provide a direct probe of physics at very high energy scales. We develop a framework for cosmic string inference from observations of the CMB made over the celestial sphere, performing a Bayesian analysis in wavelet space where the string-induced CMB component has distinct statistical properties to the standard inflationary component. Our wavelet-Bayesian framework provides a principled approach to compute the posterior distribution of the string tension Gµ and the Bayesian evidence ratio comparing the string model to the standard inflationary model. Furthermore, we present a technique to recover an estimate of any string-induced CMB map embedded in observational data. Using Planck-like simulations we demonstrate the application of our framework and evaluate its performance. The method is sensitive to Gµ ∼ 5 × 10 −7 for Nambu-Goto string simulations that include an integrated Sachs-Wolfe (ISW) contribution only and do not include any recombination effects, before any parameters of the analysis are optimised. The sensitivity of the method compares favourably with other techniques applied to the same simulations.

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“…These new wavelets have been applied successfully to the detection of point sources, but the full potential of the method has not yet been analyzed. On the other hand, a new class of discrete spherical wavelets, called needlets, has been introduced [7,25]. These functions are derived by combining three ideas, namely, a Littlewood-Paley decomposition, a suitable distribution of (finitely many) points on the sphere, called centers, and an exact quadrature rule.…”

Section: Recent Developmentsmentioning

confidence: 99%