# A scale-space approach with wavelets to singularity estimation

ESAIM: Probability and Statistics (2005)

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

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topBigot, Jérémie. "A scale-space approach with wavelets to singularity estimation." ESAIM: Probability and Statistics 9 (2005): 143-164. <http://eudml.org/doc/245802>.

@article{Bigot2005,

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},

language = {eng},

pages = {143-164},

publisher = {EDP-Sciences},

title = {A scale-space approach with wavelets to singularity estimation},

url = {http://eudml.org/doc/245802},

volume = {9},

year = {2005},

}

TY - JOUR

AU - Bigot, Jérémie

TI - A scale-space approach with wavelets to singularity estimation

JO - ESAIM: Probability and Statistics

PY - 2005

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

UR - http://eudml.org/doc/245802

ER -

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