Efficient Optimal Reconstruction of Linear Fields and Band-powers from Cosmological Data

Abstract

We present an efficient implementation of Wiener filtering of real-space linear field and optimal quadratic estimator of its power spectrum Band-powers. We first recast the field reconstruction into an optimization problem, which we solve using quasi-Newton optimization. We then recast the power spectrum estimation into the field marginalization problem, from which we obtain an expression that depends on the field reconstruction solution and a determinant term. We develop a novel simulation based method for the latter. We extend the simulations formalism to provide the covariance matrix for the power spectrum. We develop a flexible framework that can be used on a variety of cosmological fields and present results for a variety of test cases, using simulated examples of projected density fields, projected shear maps from galaxy lensing, and observed Cosmic Microwave Background (CMB) temperature anisotropies, with a wide range of map incompleteness and variable noise. For smaller cases where direct numerical inversion is possible, we show that our solution matches that created by direct Wiener Filtering at a fraction of the overall computation cost. Even more significant reduction of computational is achieved by this implementation of optimal quadratic estimator due to the fast evaluation of the Hessian matrix. This technique allows for accurate map and power spectrum reconstruction with complex masks and nontrivial noise properties.

arXiv comment23 pages, 14 figures

References in corpus (38)

• Planck 2015 results. XIII. Cosmological parameters
• HEALPix -- a Framework for High Resolution Discretization, and Fast Analysis of Data Distributed on the Sphere
• Weak Gravitational Lensing
• A Method for Weak Lensing Observations
• Planck 2015 results. XI. CMB power spectra, likelihoods, and robustness of parameters
• Mass Reconstruction with CMB Polarization
• A high resolution foreground cleaned CMB map from WMAP
• Intrinsic alignment-lensing interference as a contaminant of cosmic shear
• Estimating the Power Spectrum of the Cosmic Microwave Background
• How to measure CMB power spectra without losing information
• Reconstruction of lensing from the cosmic microwave background polarization
• Cosmological Model Predictions for Weak Lensing: Linear and Nonlinear Regimes
• Bayesian physical reconstruction of initial conditions from large scale structure surveys
• The Intrinsic Alignment of Galaxies and its Impact on Weak Gravitational Lensing in an Era of Precision Cosmology
• Measuring primordial non-Gaussianity in the cosmic microwave background
• B-modes in cosmic shear from source redshift clustering
• Cosmic Shear Statistics and Cosmology
• ELUCID - Exploring the Local Universe with reConstructed Initial Density field I: Hamiltonian Markov Chain Monte Carlo Method with Particle Mesh Dynamics
• Application of Monte Carlo Algorithms to the Bayesian Analysis of the Cosmic Microwave Background
• Bayesian reconstruction of the cosmological large-scale structure: methodology, inverse algorithms and numerical optimization
• Towards optimal extraction of cosmological information from nonlinear data
• Maximum a posteriori CMB lensing reconstruction
• Hierarchical Cosmic Shear Power Spectrum Inference
• Reconstruction of signals with unknown spectra in information field theory with parameter uncertainty
• Mining Weak Lensing Surveys
• Cosmological parameters, shear maps and power spectra from CFHTLenS using Bayesian hierarchical inference
• Efficient Wiener filtering without preconditioning
• Unfolding the matter distribution using 3-D weak gravitational lensing
• Improving Weak Lensing Mass Map Reconstructions using Gaussian and Sparsity Priors: Application to DES SV
• The Wiener-Filtered COBE DMR Data and Predictions for the Tenerife Experiment
• Cosmography and Power Spectrum Estimation: a Unified Approach
• Reconstructing Small Scale Lenses from the Cosmic Microwave Background Temperature Fluctuations
• Bayesian weak lensing tomography: Reconstructing the 3D large-scale distribution of matter with a lognormal prior
• Multi-resolution Bayesian CMB component separation through Wiener-filtering with a pseudo-inverse preconditioner
• Wiener filter reloaded: fast signal reconstruction without preconditioning
• Density mapping with weak lensing and phase information
• Improving three-dimensional mass mapping with weak gravitational lensing using galaxy clustering
• Solving linear equations with messenger-field and conjugate gradients techniques - an application to CMB data analysis

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