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Thesis Defense

Multifractal analysis for multivariate data with application to remote sensing

Sébastien COMBREXELLE - Team SC - IRIT

Wednesday 12 October 2016, 10h00
INP-ENSEEIHT, Salle des thèses
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Patrice Abry, CNRS, Directeur de recherche, Examinateur
Laure Blanc-Féraud, CNRS, Directeur de recherche, Examinateur
Philippe Ciuciu, CEA, Directeur de recherche, Rapporteur
Stephen McLaughlin, Professeur à l'Université Heriot-Watt, Co-directeur de thèse
Gabriel Peyré, CNRS, Directeur de recherche, Rapporteur
Véronique Serfaty, Scientifique DGA - Responsable domaine, Examinateur
Jean-Yves Tourneret, Professeur à l'INPT-ENSEEIHT, Directeur de thèse
Herwig Wendt, CNRS, Chargé de recherche, Encadrant de thèse
Victoria Cox, Chercheuse DSTL, Invité


Texture characterization is a central element in many image processing applications. Texture analysis can be embedded in the mathematical framework of multifractal analysis, enabling the study of the fluctuations in regularity of image intensity and providing practical tools for their assessment, the wavelet coefficients or wavelet leaders. Although successfully applied in various contexts, multifractal analysis suffers at present from two major limitations. First, the accurate estimation of multifractal parameters for image texture remains a challenge, notably for small image sizes. Second, multifractal analysis has so far been limited to the analysis of a single image, while the data available in applications are increasingly multivariate.
The main goal of this thesis is to develop practical contributions to overcome these limitations. The first limitation is tackled by introducing a generic statistical model for the logarithm of wavelet leaders, parametrized by multifractal parameters of interest. This statistical model enables us to counterbalance the variability induced by small sample sizes and to embed the estimation in a Bayesian framework. This yields robust and accurate estimation procedures, effective both for small and large images. The multifractal analysis of multivariate images is then addressed by generalizing this Bayesian framework to hierarchical models able to account for the assumption that multifractal properties evolve smoothly in the dataset. This is achieved via the design of suitable priors relating the dynamical properties of the multifractal parameters of the different components composing the dataset. Different priors are investigated and compared in this thesis by means of numerical simulations conducted on synthetic multivariate multifractal images. This work is further completed by the investigation of the potential benefits of multifractal analysis and the proposed Bayesian methodology for remote sensing via the example of hyperspectral imaging.