Minimizing travelling waves for the one-dimensional nonlinear Schr\"odinger equation with non-zero condition at infinity

This paper deals with the existence of travelling wave solutions for a general one-dimensional nonlinear Schr\"odinger equation. We construct these solutions by minimizing the energy under the constraint of fixed momentum. We also prove that the family of minimizers is stable. Our method is based on recent articles about the orbital stability for the classical and non-local Gross-Pitaevskii equations [3, 10]. It relies on a concentration-compactness theorem, which provides some compactness for the minimizing sequences and thus the convergence (up to a subsequence) towards a travelling wave solution

Indexation d'images texturées fondée sur le modèle multivarié de la Gaussienne généralisée asymétrique à copule Gaussienne

National audienceDans ce papier, nous nous intéressons à l'indexation d'images texturées dans le contexte des modèles probabilistes multivariés. En utilisant une transformée en ondelettes, la dépendance entre les coefficients des sous-bandes peut être caractérisée à l'aide d'un modèle stochastique multivarié. Nous introduisons le modèle multivarié de la Gaussienne généralisée asymétrique à copule Gaussienne (GC-MAGG) pour la caractérisation de la dépendance spatiale des coefficients d'ondelettes en prenant en compte l'éventuelle asymétrie de leurs distributions marginales. Le modèle proposé est validé en utilisant un test statistique d'adéquation aux statistiques jointes observées. L'expression analytique de la divergence de Jeffreys entre deux distributions à copule Gaussienne est calculée afin de mesurer la similarité et utiliser le modèle proposé dans une application de classification d'images. En comparaison avec d'autres modèles de la littérature, des bonnes performances sont obtenues en recherche d'images par contenu textural en utilisant le modèle proposé GC-MAGG

Stochasticity: A Feature for the Structuring of Large and Heterogeneous Image Databases

International audienceThe paper addresses image feature characterization and the structuring of large and heterogeneous image databases through the stochasticity or randomness appearance. Measuring stochasticity involves finding suitable representations that can significantly reduce statistical dependencies of any order. Wavelet packet representations provide such a framework for a large class of stochastic processes through an appropriate dictionary of parametric models. From this dictionary and the Kolmogorov stochasticity index, the paper proposes semantic stochasticity templates upon wavelet packet sub-bands in order to provide high level classification and content-based image retrieval. The approach is shown to be relevant for texture images

Multi-Date Divergence Matrices for the Analysis of SAR Image Time Series

International audienceThe paper provides a spatio-temporal change detection framework for the analysis of image time series. In this framework, the detection of changes in time is addressed at the image level by using a matrix of cross-dissimilarities computed upon wavelet and curvelet image features. This makes possible identifying the acquisitions-of-interest: the acquisitions that exhibit singular behavior with respect to their neighborhood in the time series and those that are representatives of some stationary behavior. These acquisitions-of-interest are compared at the pixel level in order to detect spatial changes characterizing the evolution of the time series. Experiments carried out over ERS and TerraSAR-X time series highlight the relevancy of the approach for analyzing SAR image time series

Performance of the maximum likelihood estimators for the parameters of multivariate generalized Gaussian distributions

International audienceThis paper studies the performance of the maximum likelihood estimators (MLE) for the parameters of multivariate generalized Gaussian distributions. When the shape parameter belongs to ]0,1[, we have proved that the scatter matrix MLE exists and is unique up to a scalar factor. After providing some elements about this proof, an estimation algorithm based on a Newton-Raphson recursion is investigated. Some experiments illustrate the convergence speed of this algorithm. The bias and consistency of the scatter matrix estimator are then studied for different values of the shape parameter. The performance of the shape parameter estimator is finally addressed by comparing its variance to the Cramér-Rao bound