Applications of Wavelets to the Analysis of Cosmic Microwave Background Maps

@article{Tenorio1999ApplicationsOW,
  title={Applications of Wavelets to the Analysis of Cosmic Microwave Background Maps},
  author={L. Tenorio and Andrew H. Jaffe and Shaul Hanany and C. Lineweaver},
  journal={Monthly Notices of the Royal Astronomical Society},
  year={1999},
  volume={310},
  pages={823-834}
}
We consider wavelets as a tool to perform a variety of tasks in the context of analyzing cosmic microwave background (CMB) maps. Using Spherical Haar Wavelets we define a position and angular-scale-dependent measure of power that can be used to assess the existence of spatial structure. We apply planar Daubechies wavelets for the identification and removal of points sources from small sections of sky maps. Our technique can successfully identify virtually all point sources which are above 3… 

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References

SHOWING 1-10 OF 24 REFERENCES

How to measure CMB power spectra without losing information

A new method for estimating the angular power spectrum C_l from cosmic microwave background (CMB) maps is presented, which has the following desirable properties: (1) It is unbeatable in the sense

Cumulants as non-Gaussian qualifiers

This work defines two new sets of statistics to quantify the level of non-Gaussianity in the cosmic microwave background and derives a series of properties concerning these statistics for a Gaussian random field and shows how one can relate these quantities to the higher order moments of temperature maps.

Evidence for Scale-Scale Correlations in the Cosmic Microwave Background Radiation

We perform a discrete wavelet analysis of the Cosmic Background Explorer differential microwave radiometer (DMR) 4-yr sky maps and find a significant scale-scale correlation on angular scales from

Combined Spherical Harmonic and Wavelet Expansion—A Future Concept in Earth's Gravitational Determination

Abstract The basic theory of spherical singular integrals is recapitulated. Criteria are given for measuring the space-frequency localization of functions on the sphere. The trade-off between “space

Signal-to-noise eigenmode analysis of the two-year COBE maps.

  • Bond
  • Physics
    Physical review letters
  • 1995
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.

Correlated Noise in the COBE DMR Sky Maps

The Cosmic Background Explorer Satellite Differential Radiometer (COBE DMR) sky maps contain low-level correlated noise. We obtain estimates of the amplitude and pattern of the correlated noise from

Wavelets and Statistics

Thresholding of Wavelet Coefficients as Multiple Hypotheses Testing Procedure and Nonparametric Supervised Image Segmentation by Energy Minimization using Wavelets are presented.

Wavelet thresholding via a Bayesian approach

We discuss a Bayesian formalism which gives rise to a type of wavelet threshold estimation in nonparametric regression. A prior distribution is imposed on the wavelet coefficients of the unknown

Wavelet Threshold Estimators for Data with Correlated Noise

Wavelet threshold estimators for data with stationary correlated noise are constructed by applying a level‐dependent soft threshold to the coefficients in the wavelet transform. A variety of

Adapting to Unknown Smoothness via Wavelet Shrinkage

Abstract We attempt to recover a function of unknown smoothness from noisy sampled data. We introduce a procedure, SureShrink, that suppresses noise by thresholding the empirical wavelet