5,926 research outputs found
Applications of Wavelets to the Analysis of Cosmic Microwave Background Maps
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 sigma and more than 80% of those above 1
sigma. We discuss the trade-offs between the levels of correct and false
detections. We denoise and compress a 100,000 pixel CMB map by a factor of
about 10 in 5 seconds achieving a noise reduction of about 35%. In contrast to
Wiener filtering the compression process is model independent and very fast. We
discuss the usefulness of wavelets for power spectrum and cosmological
parameter estimation. We conclude that at present wavelet functions are most
suitable for identifying localized sources.Comment: 10 pages, 6 figures. Submitted to MNRA
Hyperanalytic denoising
A new threshold rule for the estimation of a deterministic image immersed in noise is proposed. The full estimation procedure is based on a separable wavelet decomposition of the observed image, and the estimation is improved by introducing the new threshold to estimate the decomposition coefficients. The observed wavelet coefficients are thresholded, using the magnitudes of wavelet transforms of a small number of "replicates" of the image. The "replicates" are calculated by extending the image into a vector-valued hyperanalytic signal. More than one hyperanalytic signal may be chosen, and either the hypercomplex or Riesz transforms are used, to calculate this object. The deterministic and stochastic properties of the observed wavelet coefficients of the hyperanalytic signal, at a fixed scale and position index, are determined. A "universal" threshold is calculated for the proposed procedure. An expression for the risk of an individual coefficient is derived. The risk is calculated explicitly when the "universal" threshold is used and is shown to be less than the risk of "universal" hard thresholding, under certain conditions. The proposed method is implemented and the derived theoretical risk reductions substantiated
Wavelet domain Bayesian denoising of string signal in the cosmic microwave background
An algorithm is proposed for denoising the signal induced by cosmic strings
in the cosmic microwave background (CMB). A Bayesian approach is taken, based
on modeling the string signal in the wavelet domain with generalized Gaussian
distributions. Good performance of the algorithm is demonstrated by simulated
experiments at arcminute resolution under noise conditions including primary
and secondary CMB anisotropies, as well as instrumental noise.Comment: 16 pages, 11 figures. Version 2 matches version accepted for
publication in MNRAS. Changes include substantial clarifications on our
approach and a significant reduction of manuscript lengt
Blind Curvelet based Denoising of Seismic Surveys in Coherent and Incoherent Noise Environments
The localized nature of curvelet functions, together with their frequency and
dip characteristics, makes the curvelet transform an excellent choice for
processing seismic data. In this work, a denoising method is proposed based on
a combination of the curvelet transform and a whitening filter along with
procedure for noise variance estimation. The whitening filter is added to get
the best performance of the curvelet transform under coherent and incoherent
correlated noise cases, and furthermore, it simplifies the noise estimation
method and makes it easy to use the standard threshold methodology without
digging into the curvelet domain. The proposed method is tested on
pseudo-synthetic data by adding noise to real noise-less data set of the
Netherlands offshore F3 block and on the field data set from east Texas, USA,
containing ground roll noise. Our experimental results show that the proposed
algorithm can achieve the best results under all types of noises (incoherent or
uncorrelated or random, and coherent noise)
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