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...
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....
High dimensional data are more and more frequent in many application fields. It becomes particularly important to be able to extract meaningful features from these data sets. Deformable template model is a popular way to achieve this. This paper is a review on the statistical aspects of this model as well as its generalizations. We describe the different mathematical frameworks to handle different data types as well as the deformations. We recall the theoretical convergence properties of the estimators...
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