Statistical modeling of polarimetric SAR data: a survey and challenges

Knowledge of the exact statistical properties of the signal plays an important role in the applications of Polarimetric Synthetic Aperture Radar (PolSAR) data. In the last three decades, a considerable research effort has been devoted to finding accurate statistical models for PolSAR data, and a number of distributions have been proposed. In order to see the differences of various models and to make a comparison among them, a survey is provided in this paper. Texture models, which could capture the non-Gaussian behavior observed in high resolution data, and yet keep a compact mathematical form, are mainly explained. Probability density functions for the single look data and the multilook data are reviewed, as well as the advantages and applicable context of those models. As a summary, challenges in the area of statistical analysis of PolSAR data are also discussed.Peer ReviewedPostprint (published version

Contributions to Vine-Copula Modeling

144 p.Regular vine-copula models (R-vines) are a powerful statistical tool for modeling thedependence structure of multivariate distribution functions. In particular, they allow modelingdierent types of dependencies among random variables independently of their marginaldistributions, which is deemed the most valued characteristic of these models. In this thesis, weinvestigate the theoretical properties of R-vines for representing dependencies and extend theiruse to solve supervised classication problems. We focus on three research directions.!In the rst line of research, the relationship between the graphical representations of R-vines!ÁREA LÍNEA1 2 0 3 0 4ÁREA LÍNEA1 2 0 3 1 7ÁREA LÍNEAÁREA LÍNEA!and Bayesian polytree networks is analyzed in terms of how conditional pairwise independence!relationships are represented by both models. In order to do that, we use an extended graphical!representation of R-vines in which the R-vine graph is endowed with further expressiveness,being possible to distinguish between edges representing independence and dependencerelationships. Using this representation, a separation criterion in the R-vine graph, called Rseparation,is dened. The proposed criterion is used in designing methods for building thegraphical structure of polytrees from that of R-vines, and vice versa. Moreover, possiblecorrespondences between the R-vine graph and the associated R-vine copula as well as dierentproperties of R-separation are analyzed. In the second research line, we design methods forlearning the graphical structure of R-vines from dependence lists. The main challenge of thistask lies in the extremely large size of the search space of all possible R-vine structures. Weprovide two strategies to solve the problem of learning R-vines that represent the largestnumber of dependencies in a list. The rst approach is a 0 -1 linear programming formulation forbuilding truncated R-vines with only two trees. The second approach is an evolutionaryalgorithm, which is able to learn complete and truncated R-vines. Experimental results show thesuccess of this strategy in solving the optimization problem posed. In the third research line, weintroduce a supervised classication approach where the dependence structure of the problemfeatures is modeled through R-vines. The ecacy of these classiers is validated in a mentaldecoding problem and in an image recognition task. While Rvines have been extensivelyapplied in elds such as economics, nance and statistics, only recently have they found theirplace in classication tasks. This contribution represents a step forward in understanding R-vinesand the prospect of extending their use to other machine learning tasks

Modélisation stochastique pour l'analyse d'images texturées (approches Bayésiennes pour la caractérisation dans le domaine des transformées)

Le travail présenté dans cette thèse s inscrit dans le cadre de la modélisation d images texturées à l aide des représentations multi-échelles et multi-orientations. Partant des résultats d études en neurosciences assimilant le mécanisme de la perception humaine à un schéma sélectif spatio-fréquentiel, nous proposons de caractériser les images texturées par des modèles probabilistes associés aux coefficients des sous-bandes. Nos contributions dans ce contexte concernent dans un premier temps la proposition de différents modèles probabilistes permettant de prendre en compte le caractère leptokurtique ainsi que l éventuelle asymétrie des distributions marginales associées à un contenu texturée. Premièrement, afin de modéliser analytiquement les statistiques marginales des sous-bandes, nous introduisons le modèle Gaussien généralisé asymétrique. Deuxièmement, nous proposons deux familles de modèles multivariés afin de prendre en compte les dépendances entre coefficients des sous-bandes. La première famille regroupe les processus à invariance sphérique pour laquelle nous montrons qu il est pertinent d associer une distribution caractéristique de type Weibull. Concernant la seconde famille, il s agit des lois multivariées à copules. Après détermination de la copule caractérisant la structure de la dépendance adaptée à la texture, nous proposons une extension multivariée de la distribution Gaussienne généralisée asymétrique à l aide de la copule Gaussienne. L ensemble des modèles proposés est comparé quantitativement en terme de qualité d ajustement à l aide de tests statistiques d adéquation dans un cadre univarié et multivarié. Enfin, une dernière partie de notre étude concerne la validation expérimentale des performances de nos modèles à travers une application de recherche d images par le contenu textural. Pour ce faire, nous dérivons des expressions analytiques de métriques probabilistes mesurant la similarité entre les modèles introduits, ce qui constitue selon nous une troisième contribution de ce travail. Finalement, une étude comparative est menée visant à confronter les modèles probabilistes proposés à ceux de l état de l art.In this thesis we study the statistical modeling of textured images using multi-scale and multi-orientation representations. Based on the results of studies in neuroscience assimilating the human perception mechanism to a selective spatial frequency scheme, we propose to characterize textures by probabilistic models of subband coefficients.Our contributions in this context consist firstly in the proposition of probabilistic models taking into account the leptokurtic nature and the asymmetry of the marginal distributions associated with a textured content. First, to model analytically the marginal statistics of subbands, we introduce the asymmetric generalized Gaussian model. Second, we propose two families of multivariate models to take into account the dependencies between subbands coefficients. The first family includes the spherically invariant processes that we characterize using Weibull distribution. The second family is this of copula based multivariate models. After determination of the copula characterizing the dependence structure adapted to the texture, we propose a multivariate extension of the asymmetric generalized Gaussian distribution using Gaussian copula. All proposed models are compared quantitatively using both univariate and multivariate statistical goodness of fit tests. Finally, the last part of our study concerns the experimental validation of the performance of proposed models through texture based image retrieval. To do this, we derive closed-form metrics measuring the similarity between probabilistic models introduced, which we believe is the third contribution of this work. A comparative study is conducted to compare the proposed probabilistic models to those of the state-of-the-art.BORDEAUX1-Bib.electronique (335229901) / SudocSudocFranceF