Wavelet denoising of Poisson-distributed data and applications

C. Charles, J. P. Rasson

Research output: Contribution to journalArticle

Abstract

In experiments, observations are often modelled as a noisy signal. If the signal is embedded in an additive Gaussian noise, its estimation is often done by finding a wavelet basis that concentrates the signal energy over few coefficients and by thresholding the noisy coefficients. However, in many problems of physics, the recorded data are not modelled by Gaussian noise but as the realisation of a Poisson process. In this case, a method of general Poisson process filtering is used. This widens the Gaussian noise filtering and is operated by a kind of frequency-and- time hard thresholding of Haar wavelet coefficients. Not only the detail coefficients are thresholded but also the coefficients related to the rough approximation. Because of the distribution of the wavelet coefficients, a pair of thresholds is proposed for each coefficient. This filtering is illustrated with spectra from different experiments. © 2003 Elsevier Science B.V. All rights reserved.

Original languageEnglish
Pages (from-to)139-148
Number of pages10
JournalComputational Statistics and Data Analysis
Volume43
Issue number2
Publication statusPublished - 28 Jun 2003

Fingerprint

Wavelet Denoising
Siméon Denis Poisson
Gaussian Noise
Coefficient
Wavelet Coefficients
Thresholding
Poisson process
Physics
Experiments
Filtering
Noise Estimation
Noise Filtering
Haar Wavelet
Wavelet Bases
Rough
Experiment
Coefficients
Wavelets
Approximation
Energy

Keywords

  • Denoising
  • Poisson process
  • Wavelets

Cite this

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Wavelet denoising of Poisson-distributed data and applications. / Charles, C.; Rasson, J. P.

In: Computational Statistics and Data Analysis, Vol. 43, No. 2, 28.06.2003, p. 139-148.

Research output: Contribution to journalArticle

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