A scale-space approach with wavelets to singularity estimation

Jérémie Bigot

ESAIM: Probability and Statistics (2010)

  • Volume: 9, page 143-164
  • ISSN: 1292-8100

Abstract

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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.

How to cite

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Bigot, Jérémie. "A scale-space approach with wavelets to singularity estimation." ESAIM: Probability and Statistics 9 (2010): 143-164. <http://eudml.org/doc/104327>.

@article{Bigot2010,
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. },
author = {Bigot, Jérémie},
journal = {ESAIM: Probability and Statistics},
keywords = {Lipschitz singularity; continuous wavelet transform; scale-space representation; zero-crossings; wavelet maxima; feature extraction; non parametric estimation; bagging; landmark-based matching.; landmark-based matching},
language = {eng},
month = {3},
pages = {143-164},
publisher = {EDP Sciences},
title = {A scale-space approach with wavelets to singularity estimation},
url = {http://eudml.org/doc/104327},
volume = {9},
year = {2010},
}

TY - JOUR
AU - Bigot, Jérémie
TI - A scale-space approach with wavelets to singularity estimation
JO - ESAIM: Probability and Statistics
DA - 2010/3//
PB - EDP Sciences
VL - 9
SP - 143
EP - 164
AB - 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.
LA - eng
KW - Lipschitz singularity; continuous wavelet transform; scale-space representation; zero-crossings; wavelet maxima; feature extraction; non parametric estimation; bagging; landmark-based matching.; landmark-based matching
UR - http://eudml.org/doc/104327
ER -

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