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A scale-space approach with wavelets to singularity estimation

Bigot, Jérémie A scale-space approach with wavelets to singularity estimation. (2005) ESAIM: Probability and Statistics, 9. 143-164. ISSN 1292-8100

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Official URL: http://dx.doi.org/10.1051/ps:2005007

Abstract

This paper is concerned with the problem of determining the typical features of a curve when it is observed with noise. It has been shown that one can characterize the Lipschitz singularities of a signal by following the propagation across scales of the modulus maxima of its continuous wavelet transform. A nonparametric approach, based on appropriate thresholding of the empirical wavelet coefficients, is proposed to estimate the wavelet maxima of a signal observed with noise at various scales. In order to identify the singularities of the unknown signal, we introduce a new tool, "the structural intensity", that computes the "density" of the location of the modulus maxima of a wavelet representation along various scales. This approach is shown to be an effective technique for detecting the significant singularities of a signal corrupted by noise and for removing spurious estimates. The asymptotic properties of the resulting estimators are studied and illustrated by simulations. An application to a real data set is also proposed.

Item Type:Article
Additional Information:Thanks to EDP Sciences editor. The definitive version is available at http://www.esaim-ps.org/action/displayAbstract?fromPage=online&aid=8212731
HAL Id:hal-00837732
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National des Sciences Appliquées de Toulouse - INSA (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
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Deposited By: Jérémie Bigot
Deposited On:14 Jun 2013 07:38

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