Fast power spectrum estimation

@article{Pen2003FastPS,
  title={Fast power spectrum estimation},
  author={Ue-li Pen},
  journal={Monthly Notices of the Royal Astronomical Society},
  year={2003},
  volume={346},
  pages={619-626}
}
  • U. Pen
  • Published 29 April 2003
  • Physics
  • Monthly Notices of the Royal Astronomical Society
We present a new algorithm to rapidly and optimally compute power spectra. This new algorithm is based on a generalization of iterative multigrid, and has computational cost O(N log N), compared to the standard brute force approach which costs O(N 3 ). The procedure retains this speed on the full sky and for ill-conditioned matrices. It is applicable to galaxy power spectra, cosmic microwave background (CMB), polarization and weak lensing data. We present a mathematical convergence analysis… 

Figures from this paper

Hybrid estimation of cosmic microwave background polarization power spectra
This paper generalizes the hybrid power spectrum estimation method developed in a previous paper to the estimation of polarization power spectra of the cosmic microwave background radiation. The
Myths and truths concerning estimation of power spectra: the case for a hybrid estimator
It is widely believed that maximum-likelihood estimators must be used to provide optimal estimates of power spectra. Since such estimators require the inversion and multiplication of N d x N d
Cosmic microwave background power spectrum estimation with non-circular beam and incomplete sky coverage
Over the last decade, measurements of the cosmic microwave background (CMB) anisotropy have spearheaded the remarkable transition of cosmology into a precision science. However, addressing the
CMB power spectrum estimation using noncircular beams
The measurements of the angular power spectrum of the Cosmic Microwave Background (CMB) anisotropy have proved crucial to the emergence of cosmology as a precision science in recent years. In this
Reconstruction of the One-Point Distribution of Convergence from Weak Lensing by Large-Scale Structure
Weak-lensing measurements are starting to provide statistical maps of the distribution of matter in the universe that are increasingly precise and complementary to cosmic microwave background maps.
Fast n-point correlation functions and three-point lensing application
TLDR
A new algorithm to rapidly compute the two-point, three-point and n -point correlation functions in roughly O( N  log  N ) time for N particles, instead of O( n n ) as required by brute force approaches.
Non-Circular beam correction to the CMB power spectrum
Abstract In the era of high precision CMB measurements, systematic effects are beginning to limit the ability to extract subtler cosmological information. The non-circularity of the experimental beam
Optimizing the computation of n-point correlations on large-scale astronomical data
TLDR
A highly-tuned npcf computation code is presented that enables a much larger 3-point correlation computation on the galaxy distribution than was previously possible, and a detailed performance evaluation on many different architectures is shown.
A method for 21 cm power spectrum estimation in the presence of foregrounds
The technique of 21 cm tomography promises to be a powerful tool for estimating cosmological parameters, constraining the epoch of reionization, and probing the so-called dark ages. However,
Global, Exact Cosmic Microwave Background Data Analysis Using Gibbs Sampling
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
...
1
2
...

References

SHOWING 1-10 OF 14 REFERENCES
An Efficient Technique to Determine the Power Spectrum from Cosmic Microwave Background Sky Maps
There is enormous potential to advance cosmology from statistical characterizations of cosmic microwave background (CMB) sky maps. The angular power spectrum of the microwave anisotropy is a
FAST COSMIC MICROWAVE BACKGROUND ANALYSES VIA CORRELATION FUNCTIONS
We propose and implement a fast, universally applicable method for extracting the angular power spectrum from cosmic microwave background temperature maps by first estimating the correlation function
Estimating the power spectrum of the cosmic microwave background
We develop two methods for estimating the power spectrum, C_l, of the cosmic microwave background (CMB) from data and apply them to the COBE/DMR and Saskatoon datasets. One method involves a direct
Power Spectra Estimation for Weak Lensing
We develop a method for estimating the shear power spectra from weak-lensing observations and test it on simulated data. Our method describes the shear field in terms of angular power spectra and the
Mining weak lensing surveys
Abstract We present a survey of the cosmological applications of the next generation of weak lensing surveys, paying special attention to the computational challenges presented by the number of
Weak Lensing Reconstruction and Power Spectrum Estimation: Minimum Variance Methods
Large-scale structure distorts the images of background galaxies, which allows one to measure directly the projected distribution of dark matter in the universe and determine its power spectrum. Here
Power spectrum analysis of three-dimensional redshift surveys
We develop a general method for power spectrum analysis of three dimensional redshift surveys. We present rigorous analytical estimates for the statistical uncertainty in the power and we are able to
The 4 Year COBE Normalization and Large-Scale Structure
We present an analysis of the 4 year data from the COBE DMR experiment. We use a Karhunen- Loeve expansion of the pixel data to calculate the normalization and goodness of -t of a range of models of
Signal-to-noise eigenmode analysis of the two-year COBE maps.
  • Bond
  • Physics, Medicine
    Physical review letters
  • 1995
TLDR
These $S/N$-eigenmodes are indispensible for rapid Bayesian analyses of anisotropy experiments, applied here to the recently-released two-year COBE {\it dmr} maps and the {\it firs} map.
Gravity and Nongravity Modes in the VIRMOS-DESCART Weak-Lensing Survey*
We analyze the weak-lensing data of the VIRMOS imaging survey using projections (called E- and B-modes) of the two independent observable correlation functions. The E-mode contains all the lensing
...
1
2
...