### 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 language | English |
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Pages (from-to) | 139-148 |

Number of pages | 10 |

Journal | Computational Statistics and Data Analysis |

Volume | 43 |

Issue number | 2 |

Publication status | Published - 28 Jun 2003 |

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### Keywords

- Denoising
- Poisson process
- Wavelets

### Cite this

*Computational Statistics and Data Analysis*,

*43*(2), 139-148.

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*Computational Statistics and Data Analysis*, vol. 43, no. 2, pp. 139-148.

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - Wavelet denoising of Poisson-distributed data and applications

AU - Charles, C.

AU - Rasson, J. P.

PY - 2003/6/28

Y1 - 2003/6/28

N2 - 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.

AB - 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.

KW - Denoising

KW - Poisson process

KW - Wavelets

UR - http://www.scopus.com/inward/record.url?scp=0038006811&partnerID=8YFLogxK

M3 - Article

VL - 43

SP - 139

EP - 148

JO - Computational Statistics and Data Analysis

JF - Computational Statistics and Data Analysis

SN - 0167-9473

IS - 2

ER -