Wiener Reconstruction of The Large Scale Structure
TL;DR: In this paper, the authors developed the Wiener filter for the purpose of reconstructing the large scale structure of the universe from noisy, sparse and incomplete data, based on a linear minimum variance solution, given data and an assumed prior model.
Abstract: The formalism of Wiener filtering is developed here for the purpose of reconstructing the large scale structure of the universe from noisy, sparse and incomplete data. The method is based on a linear minimum variance solution, given data and an assumed \prior model which specifies the covariance matrix of the field to be reconstructed. While earlier applications of the Wiener filter have focused on estimation, namely suppressing the noise in the measured quantities, we extend the method here to perform both prediction and dynamical reconstruction. The Wiener filter is used to predict the values of unmeasured quantities, such as the density field in un-sampled regions of space, or to deconvolve blurred data. The method is developed, within the context of linear gravitational instability theory, to perform dynamical reconstruction of one field which is dynamically related to some other observed field. This is the case, for example, in the reconstruction of the real space galaxy distribution from its redshift distribution When the field to be reconstructed is a Gaussian random field, such as the primordial perturbation field predicted by the canonical model of cosmology, the Wiener filter can be pushed to its fullest potential. In such a case the Wiener estimator coincides with the Bayesian estimator designed to maximize the {\it posterior} probability. The Wiener filter can be also derived by assuming a quadratic regularization function, in analogy with the `Maximum Entropy' method. The mean field obtained by the minimal variance solution can be supplemented with constrained realizations of the Gaussian field to
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Harvard University1, Texas A&M University2, University of Portsmouth3, South East Physics Network4, California Institute of Technology5, Microsoft6, University College London7, Stanford University8, University of Southern California9, University of Massachusetts Amherst10, University of Virginia11, McKinsey & Company12
TL;DR: The 2MASS XSC as mentioned in this paper contains nearly a million galaxies with K_s ≤ 13.5 mag and is essentially complete and mostly unaffected by interstellar extinction and stellar confusion down to a galactic latitude of |b| = 5° for bright galaxies.
Abstract: We present the results of the 2MASS Redshift Survey (2MRS), a ten-year project to map the full three-dimensional distribution of galaxies in the nearby universe. The Two Micron All Sky Survey (2MASS) was completed in 2003 and its final data products, including an extended source catalog (XSC), are available online. The 2MASS XSC contains nearly a million galaxies with K_s ≤ 13.5 mag and is essentially complete and mostly unaffected by interstellar extinction and stellar confusion down to a galactic latitude of |b| = 5° for bright galaxies. Near-infrared wavelengths are sensitive to the old stellar populations that dominate galaxy masses, making 2MASS an excellent starting point to study the distribution of matter in the nearby universe. We selected a sample of 44,599 2MASS galaxies with K_s ≤ 11.75 mag and |b| ≥ 5° (≥8° toward the Galactic bulge) as the input catalog for our survey. We obtained spectroscopic observations for 11,000 galaxies and used previously obtained velocities for the remainder of the sample to generate a redshift catalog that is 97.6% complete to well-defined limits and covers 91% of the sky. This provides an unprecedented census of galaxy (baryonic mass) concentrations within 300 Mpc. Earlier versions of our survey have been used in a number of publications that have studied the bulk motion of the Local Group, mapped the density and peculiar velocity fields out to 50 h^(–1) Mpc, detected galaxy groups, and estimated the values of several cosmological parameters. Additionally, we present morphological types for a nearly complete sub-sample of 20,860 galaxies with K_s ≤ 11.25 mag and |b| ≥ 10°.
643 citations
Cites methods from "Wiener Reconstruction of The Large ..."
...Sophisticated techniques were developed to analyze these surveys (Dekel et al. 1990; Zaroubi et al. 1995) but despite reasonable data and thorough analyses, the source of the CMB dipole was not convincingly identified and there remained very significant conflicts between the results of different…...
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TL;DR: In this paper, an independent foreground analysis of the Wilkinson Microwave Anisotropy Probe (WMAP) maps is performed to produce a cleaned cosmic microwave background (CMB) map, which is useful for cross-correlation with, e.g., galaxy and x-ray maps.
Abstract: We perform an independent foreground analysis of the Wilkinson Microwave Anisotropy Probe (WMAP) maps to produce a cleaned cosmic microwave background (CMB) map (available online) useful for cross-correlation with, e.g., galaxy and x-ray maps. We use a variant of the Tegmark-Efstathiou technique that assumes that the CMB has a blackbody spectrum, but is otherwise completely blind, making no assumptions about the CMB power spectrum, the foregrounds, WMAP detector noise or external templates. Compared with the foreground-cleaned internal linear combination map produced by the WMAP team, our map has the advantage of containing less non-CMB power (from foregrounds and detector noise) outside the Galactic plane. The difference is most important on the angular scale of the first acoustic peak and below, since our cleaned map is at the highest ${(12.6}^{\ensuremath{'}})$ rather than lowest ${(49.2}^{\ensuremath{'}})$ WMAP resolution. We also produce a Wiener filtered CMB map, representing our best guess as to what the CMB sky actually looks like, as well as CMB-free maps at the five WMAP frequencies useful for foreground studies. We argue that our CMB map is clean enough that the lowest multipoles can be measured without any galaxy cut, and obtain a quadrupole value that is slightly less low than that from the cut-sky WMAP team analysis. This can be understood from a map of the CMB quadrupole, which shows much of its power falling within the Galaxy cut region, seemingly coincidentally. Intriguingly, both the quadrupole and the octopole are seen to have power suppressed along a particular spatial axis, which lines up between the two, roughly towards $(l,b)\ensuremath{\sim}(\ensuremath{-}110\ifmmode^\circ\else\textdegree\fi{},60\ifmmode^\circ\else\textdegree\fi{})$ in Virgo.
612 citations
TL;DR: The zobov algorithm is described, and the results from its application to the dark matter particles in a region of the Millennium simulation are described, including an interesting high-density peak in the probability distribution of dark matter particle densities.
Abstract: zobov (ZOnes Bordering On Voidness) is an algorithm that finds density depressions in a set of points, without any free parameters, or assumptions about shape. It uses the Voronoi tessellation to estimate densities, which it uses to find both voids and subvoids. It also measures probabilities that each void or subvoid arises from Poisson fluctuations. This paper describes the zobov algorithm, and the results from its application to the dark matter particles in a region of the Millennium simulation. Additionally, the paper points out an interesting high-density peak in the probability distribution of dark matter particle densities.
328 citations
Cites background from "Wiener Reconstruction of The Large ..."
...Or, perhas optimally, it could be estimated through a constrained realization (Bertschinger 1987; Hoffman & Ribak 1991; Zaroubi et al. 1995; van de Weygaert & Bertschinger 1996)....
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TL;DR: A map of structure made using a catalogue of peculiar velocities is reported, finding locations where peculiar velocity flows diverge, as water does at watershed divides, and defining a supercluster to be the volume within such a surface, which is the extent of their home superclusters, which the authors call Laniakea.
Abstract: Galaxies congregate in clusters and along filaments, and are missing from large regions referred to as voids. These structures are seen in maps derived from spectroscopic surveys that reveal networks of structure that are interconnected with no clear boundaries. Extended regions with a high concentration of galaxies are called 'superclusters', although this term is not precise. There is, however, another way to analyse the structure. If the distance to each galaxy from Earth is directly measured, then the peculiar velocity can be derived from the subtraction of the mean cosmic expansion, the product of distance times the Hubble constant, from observed velocity. The peculiar velocity is the line-of-sight departure from the cosmic expansion and arises from gravitational perturbations; a map of peculiar velocities can be translated into a map of the distribution of matter. Here we report a map of structure made using a catalogue of peculiar velocities. We find locations where peculiar velocity flows diverge, as water does at watershed divides, and we trace the surface of divergent points that surrounds us. Within the volume enclosed by this surface, the motions of galaxies are inward after removal of the mean cosmic expansion and long range flows. We define a supercluster to be the volume within such a surface, and so we are defining the extent of our home supercluster, which we call Laniakea.
285 citations
TL;DR: In this article, an efficient and exact method that enables global Bayesian analysis of cosmic microwave background (CMB) data is described. But the method does not hinge on special assumptions about the survey geometry or noise properties, etc., it is based on a Monte Carlo approach and hence parallelizes trivially.
Abstract: We describe an efficient and exact method that enables global Bayesian analysis of cosmic microwave background (CMB) data. The method reveals the joint posterior density (or likelihood for flat priors) of the power spectrum ${C}_{\ensuremath{\ell}}$ and the CMB signal. Foregrounds and instrumental parameters can be simultaneously inferred from the data. The method allows the specification of a wide range of foreground priors. We explicitly show how to propagate the non-Gaussian dependency structure of the ${C}_{\ensuremath{\ell}}$ posterior through to the posterior density of the parameters. If desired, the analysis can be coupled to theoretical (cosmological) priors and can yield the posterior density of cosmological parameter estimates directly from the time-ordered data. The method does not hinge on special assumptions about the survey geometry or noise properties, etc., It is based on a Monte Carlo approach and hence parallelizes trivially. No trace or determinant evaluations are necessary. The feasibility of this approach rests on the ability to solve the systems of linear equations which arise. These are of the same size and computational complexity as the map-making equations. We describe a preconditioned conjugate gradient technique that solves this problem and demonstrate in a numerical example that the computational time required for each Monte Carlo sample scales as ${n}_{p}^{3/2}$ with the number of pixels ${n}_{p}$. We use our method to analyze the data from the Differential Microwave Radiometer on the Cosmic Background Explorer and explore the non-Gaussian joint posterior density of the ${C}_{\ensuremath{\ell}}$ from the Differential Microwave Radiometer on the Cosmic Background Explorer in several projections.
246 citations
References
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Book•
01 Jan 1966
TL;DR: In this article, the authors present a model for vector analysis based on the Calculus of Variations and the Sturm-Liouville theory, which includes the following: Curved Coordinates, Tensors.
Abstract: Vector Analysis. Curved Coordinates, Tensors. Determinants and Matrices. Group Theory. Infinite Series. Functions of a Complex Variable I. Functions of a Complex Variable II. Differential Equations. Sturm-Liouville Theory. Gamma-Factrial Function. Bessel Functions. Legendre Functions. Special Functions. Fourier Series. Integral Transforms. Integral Equations. Calculus of Variations. Nonlinear Methods and Chaos.
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"Wiener Reconstruction of The Large ..." refers background in this paper
...In several cases one might be interested in creating a random realizations of a GRF which reproduces a given set of data points, the so-called technique of constrained realizations (CR) (Hooman and Ribak 1991, hereafter HR)....
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...As mentioned before, the WF has its limitations, even in the framework of GRFs....
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...Thus, to the extent that the system under consideration is well described by the formalism of GRFs one might reasonably expect the WF to perform well....
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...However, until recently it has not been applied to the reconstruction of the LSS, and in particular, within the framework of GRFs....
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...The Bayesian approach, which in the case of GRFs coincides with the minimal variance solutions, provides one with a unied way of estimating both parameters of a model and a particular realization of the eld....
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01 Jan 1977
933 citations
"Wiener Reconstruction of The Large ..." refers methods in this paper
...An ad hoc attempt to correct for this conservative approach is given by a modiied WF (cf., Andrews and Hunt, 1977), which in the case of a diagonal WF has a simple form....
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Harvard University1, Texas A&M University2, University of Portsmouth3, South East Physics Network4, California Institute of Technology5, Microsoft6, University College London7, Stanford University8, University of Southern California9, University of Massachusetts Amherst10, University of Virginia11, McKinsey & Company12
TL;DR: The 2MASS XSC as mentioned in this paper contains nearly a million galaxies with K_s ≤ 13.5 mag and is essentially complete and mostly unaffected by interstellar extinction and stellar confusion down to a galactic latitude of |b| = 5° for bright galaxies.
Abstract: We present the results of the 2MASS Redshift Survey (2MRS), a ten-year project to map the full three-dimensional distribution of galaxies in the nearby universe. The Two Micron All Sky Survey (2MASS) was completed in 2003 and its final data products, including an extended source catalog (XSC), are available online. The 2MASS XSC contains nearly a million galaxies with K_s ≤ 13.5 mag and is essentially complete and mostly unaffected by interstellar extinction and stellar confusion down to a galactic latitude of |b| = 5° for bright galaxies. Near-infrared wavelengths are sensitive to the old stellar populations that dominate galaxy masses, making 2MASS an excellent starting point to study the distribution of matter in the nearby universe. We selected a sample of 44,599 2MASS galaxies with K_s ≤ 11.75 mag and |b| ≥ 5° (≥8° toward the Galactic bulge) as the input catalog for our survey. We obtained spectroscopic observations for 11,000 galaxies and used previously obtained velocities for the remainder of the sample to generate a redshift catalog that is 97.6% complete to well-defined limits and covers 91% of the sky. This provides an unprecedented census of galaxy (baryonic mass) concentrations within 300 Mpc. Earlier versions of our survey have been used in a number of publications that have studied the bulk motion of the Local Group, mapped the density and peculiar velocity fields out to 50 h^(–1) Mpc, detected galaxy groups, and estimated the values of several cosmological parameters. Additionally, we present morphological types for a nearly complete sub-sample of 20,860 galaxies with K_s ≤ 11.25 mag and |b| ≥ 10°.
643 citations