26,623 research outputs found
Reconstruction from anisotropic random measurements
Random matrices are widely used in sparse recovery problems, and the relevant
properties of matrices with i.i.d. entries are well understood. The current
paper discusses the recently introduced Restricted Eigenvalue (RE) condition,
which is among the most general assumptions on the matrix, guaranteeing
recovery. We prove a reduction principle showing that the RE condition can be
guaranteed by checking the restricted isometry on a certain family of
low-dimensional subspaces. This principle allows us to establish the RE
condition for several broad classes of random matrices with dependent entries,
including random matrices with subgaussian rows and non-trivial covariance
structure, as well as matrices with independent rows, and uniformly bounded
entries.Comment: 30 Page
The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: tomographic BAO analysis of DR12 combined sample in configuration space
We perform a tomographic baryon acoustic oscillations analysis using the
two-point galaxy correlation function measured from the combined sample of BOSS
DR12, which covers the redshift range of . Splitting the sample
into multiple overlapping redshift slices to extract the redshift information
of galaxy clustering, we obtain a measurement of and at
nine effective redshifts with the full covariance matrix calibrated using
MultiDark-Patchy mock catalogues. Using the reconstructed galaxy catalogues, we
obtain the precision of for and for
. To quantify the gain from the tomographic information, we compare
the constraints on the cosmological parameters using our 9-bin BAO
measurements, the consensus 3-bin BAO and RSD measurements at three effective
redshifts in \citet{Alam2016}, and the non-tomographic (1-bin) BAO measurement
at a single effective redshift. Comparing the 9-bin with 1-bin constraint
result, it can improve the dark energy Figure of Merit by a factor of 1.24 for
the Chevallier-Polarski-Linder parametrisation for equation of state parameter
. The errors of and from 9-bin constraints are slightly
improved when compared to the 3-bin constraint result.Comment: 14 pages, 21 figures, 7 Tables. Submitted to MNRA
Modeling the reconstructed BAO in Fourier space
The density field reconstruction technique, which was developed to partially
reverse the nonlinear degradation of the Baryon Acoustic Oscillation (BAO)
feature in the galaxy redshift surveys, has been successful in substantially
improving the cosmology constraints from recent galaxy surveys such as Baryon
Oscillation Spectroscopic Survey (BOSS). We estimate the efficiency of the
reconstruction method as a function of various reconstruction details. To
directly quantify the BAO information in nonlinear density fields before and
after reconstruction, we calculate the cross-correlations (i.e., propagators)
of the pre(post)-reconstructed density field with the initial linear field
using a mock galaxy sample that is designed to mimic the clustering of the BOSS
CMASS galaxies. The results directly provide the BAO damping as a function of
wavenumber that can be implemented into the Fisher matrix analysis. We focus on
investigating the dependence of the propagator on a choice of smoothing filters
and on two major different conventions of the redshift-space density field
reconstruction that have been used in literature. By estimating the BAO
signal-to-noise for each case, we predict constraints on the angular diameter
distance and Hubble parameter using the Fisher matrix analysis. We thus
determine an optimal Gaussian smoothing filter scale for the signal-to-noise
level of the BOSS CMASS. We also present appropriate BAO fitting models for
different reconstruction methods based on the first and second order Lagrangian
perturbation theory in Fourier space. Using the mock data, we show that the
modified BAO fitting model can substantially improve the accuracy of the BAO
position in the best fits as well as the goodness of the fits.Comment: 21 pages, 7 figures, 1 table. Minor revisions. Matches version
accepted by MNRA
The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey : measuring DA and H at z = 0.57 from the baryon acoustic peak in the Data Release 9 spectroscopic Galaxy sample
We present measurements of the angular diameter distance to and Hubble parameter at z = 0.57 from the measurement of the baryon acoustic peak in the correlation of galaxies from the Sloan Digital Sky Survey III Baryon Oscillation Spectroscopic Survey. Our analysis is based on a sample from Data Release 9 of 264 283 galaxies over 3275 square degrees in the redshift range 0.43 < z < 0.70. We use two different methods to provide robust measurement of the acoustic peak position across and along the line of sight in order to measure the cosmological distance scale. We find DA(0.57) = 1408 ± 45âMpc and H(0.57) = 92.9 ± 7.8âkmâsâ1âMpcâ1 for our fiducial value of the sound horizon. These results from the anisotropic fitting are fully consistent with the analysis of the spherically averaged acoustic peak position presented in Anderson et al. Our distance measurements are a close match to the predictions of the standard cosmological model featuring a cosmological constant and zero spatial curvature.Publisher PDFPeer reviewe
Joint space aspect reconstruction of wide-angle SAR exploiting sparsity
In this paper we present an algorithm for wide-angle synthetic aperture radar (SAR) image formation. Reconstruction of wide-angle SAR holds a promise of higher resolution and better information about a scene, but it also poses a number of challenges when compared to the traditional narrow-angle SAR. Most prominently, the isotropic point scattering model is no longer valid. We present an algorithm capable of producing high resolution reïŹectivity maps in both space and aspect, thus accounting for the anisotropic scattering behavior of targets. We pose the problem as a non-parametric three-dimensional inversion problem, with two constraints: magnitudes of the backscattered power are highly correlated across closely spaced look angles and the backscattered power
originates from a small set of point scatterers. This approach considers jointly all scatterers in the scene across all azimuths, and exploits the sparsity of the underlying scattering ïŹeld. We implement the algorithm and present
reconstruction results on realistic data obtained from the XPatch Backhoe dataset
Measuring D_A and H at z=0.35 from the SDSS DR7 LRGs using baryon acoustic oscillations
We present measurements of the angular diameter distance D_A(z) and the
Hubble parameter H(z) at z=0.35 using the anisotropy of the baryon acoustic
oscillation (BAO) signal measured in the galaxy clustering distribution of the
Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7) Luminous Red Galaxies
(LRG) sample. Our work is the first to apply density-field reconstruction to an
anisotropic analysis of the acoustic peak. Reconstruction partially removes the
effects of non-linear evolution and redshift-space distortions in order to
sharpen the acoustic signal. We present the theoretical framework behind the
anisotropic BAO signal and give a detailed account of the fitting model we use
to extract this signal from the data. Our method focuses only on the acoustic
peak anisotropy, rather than the more model-dependent anisotropic information
from the broadband power. We test the robustness of our analysis methods on 160
LasDamas DR7 mock catalogues and find that our models are unbiased at the ~0.2%
level in measuring the BAO anisotropy. After reconstruction we measure
D_A(z=0.35)=1050+/-38 Mpc and H(z=0.35)=84.4+/-7.0 km/s/Mpc assuming a sound
horizon of r_s=152.76 Mpc. Note that these measurements are correlated with a
correlation coefficient of 0.58. This represents a factor of 1.4 improvement in
the error on D_A relative to the pre-reconstruction case; a factor of 1.2
improvement is seen for H.Comment: 30 pages, 21 figures, accepted by MNRAS, updated to version accepted
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