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.
Mots-clés : Lipschitz singularity, continuous wavelet transform, scale-space representation, zero-crossings, wavelet maxima, feature extraction, non parametric estimation, bagging, landmark-based matching
@article{PS_2005__9__143_0,
author = {Bigot, J\'er\'emie},
title = {A scale-space approach with wavelets to singularity estimation},
journal = {ESAIM: Probability and Statistics},
pages = {143--164},
publisher = {EDP-Sciences},
volume = {9},
year = {2005},
doi = {10.1051/ps:2005007},
mrnumber = {2148964},
zbl = {1136.62030},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ps:2005007/}
}
TY - JOUR AU - Bigot, Jérémie TI - A scale-space approach with wavelets to singularity estimation JO - ESAIM: Probability and Statistics PY - 2005 SP - 143 EP - 164 VL - 9 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps:2005007/ DO - 10.1051/ps:2005007 LA - en ID - PS_2005__9__143_0 ER -
Bigot, Jérémie. A scale-space approach with wavelets to singularity estimation. ESAIM: Probability and Statistics, Tome 9 (2005), pp. 143-164. doi : 10.1051/ps:2005007. http://www.numdam.org/articles/10.1051/ps:2005007/
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