19,523 research outputs found
PCA detection and denoising of Zeeman signatures in stellar polarised spectra
Our main objective is to develop a denoising strategy to increase the signal
to noise ratio of individual spectral lines of stellar spectropolarimetric
observations.
We use a multivariate statistics technique called Principal Component
Analysis. The cross-product matrix of the observations is diagonalized to
obtain the eigenvectors in which the original observations can be developed.
This basis is such that the first eigenvectors contain the greatest variance.
Assuming that the noise is uncorrelated a denoising is possible by
reconstructing the data with a truncated basis. We propose a method to identify
the number of eigenvectors for an efficient noise filtering.
Numerical simulations are used to demonstrate that an important increase of
the signal to noise ratio per spectral line is possible using PCA denoising
techniques. It can be also applied for detection of magnetic fields in stellar
atmospheres. We analyze the relation between PCA and commonly used well-known
techniques like line addition and least-squares deconvolution. Moreover, PCA is
very robust and easy to compute.Comment: accepted to be published in A&
Wavelets Applied to CMB Maps: a Multiresolution Analysis for Denoising
Analysis and denoising of Cosmic Microwave Background (CMB) maps are
performed using wavelet multiresolution techniques. The method is tested on
maps with resolution resembling the
experimental one expected for future high resolution space observations.
Semianalytic formulae of the variance of wavelet coefficients are given for the
Haar and Mexican Hat wavelet bases. Results are presented for the standard Cold
Dark Matter (CDM) model. Denoising of simulated maps is carried out by removal
of wavelet coefficients dominated by instrumental noise. CMB maps with a
signal-to-noise, , are denoised with an error improvement factor
between 3 and 5. Moreover we have also tested how well the CMB temperature
power spectrum is recovered after denoising. We are able to reconstruct the
's up to with errors always below in cases with
.Comment: latex file 9 pages + 5 postscript figures + 1 gif figure (figure 6),
to be published in MNRA
Noise subspaces subtraction in SVD based on the difference of variance values
As a matrix decomposition method, Singular Value Decomposition (SVD) is introduced to signal processing such as denoising. Firstly, a polluted signal is constructed in Hankel matrix form, and then through SVD the Hankel matrix is decomposed to two unitary matrices and a diagonal matrix in which a series of singular values are arranged in a descending order. These singular values are considered to be located in a series of subspaces including signal subspaces and noise subspaces. The singular values in these subspaces are different because the signal magnitudes dominate noise magnitudes. Therefore, if these two kinds of subspaces are well separated, an ideal denoised signal could be achieved by reconstruction. This paper improves the traditional SVD denoising which merely does well in processing periodic signals’ subspaces separation. The improved SVD denoising method based on variance value extends SVD denoising to aperiodic signal denoising. The denoising results by improved SVD denoising, traditional SVD denoising, wavelet thresholding and EEMD denoising are compared and the improved SVD denoising method received an excellent numerical experimental effects
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)
MDL Denoising Revisited
We refine and extend an earlier MDL denoising criterion for wavelet-based
denoising. We start by showing that the denoising problem can be reformulated
as a clustering problem, where the goal is to obtain separate clusters for
informative and non-informative wavelet coefficients, respectively. This
suggests two refinements, adding a code-length for the model index, and
extending the model in order to account for subband-dependent coefficient
distributions. A third refinement is derivation of soft thresholding inspired
by predictive universal coding with weighted mixtures. We propose a practical
method incorporating all three refinements, which is shown to achieve good
performance and robustness in denoising both artificial and natural signals.Comment: Submitted to IEEE Transactions on Information Theory, June 200
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