Change detection in multisensor SAR images using bivariate gamma distributions

This paper studies a family of distributions constructed from multivariate gamma distributions to model the statistical properties of multisensor synthetic aperture radar (SAR) images. These distributions referred to as multisensor multivariate gamma distributions (MuMGDs) are potentially interesting for detecting changes in SAR images acquired by different sensors having different numbers of looks. The first part of the paper compares different estimators for the parameters of MuMGDs. These estimators are based on the maximum likelihood principle, the method of inference function for margins and the method of moments. The second part of the paper studies change detection algorithms based on the estimated correlation coefficient of MuMGDs. Simulation results conducted on synthetic and real data illustrate the performance of these change detectors

Isotropic Multiple Scattering Processes on Hyperspheres

This paper presents several results about isotropic random walks and multiple scattering processes on hyperspheres ${\mathbb S}^{p-1}$. It allows one to derive the Fourier expansions on ${\mathbb S}^{p-1}$ of these processes. A result of unimodality for the multiconvolution of symmetrical probability density functions (pdf) on ${\mathbb S}^{p-1}$ is also introduced. Such processes are then studied in the case where the scattering distribution is von Mises Fisher (vMF). Asymptotic distributions for the multiconvolution of vMFs on ${\mathbb S}^{p-1}$ are obtained. Both Fourier expansion and asymptotic approximation allows us to compute estimation bounds for the parameters of Compound Cox Processes (CCP) on ${\mathbb S}^{p-1}$.Comment: 16 pages, 4 figure

Pairwise likelihood estimation for multivariate mixed Poisson models generated by Gamma intensities

Estimating the parameters of multivariate mixed Poisson models is an important problem in image processing applications, especially for active imaging or astronomy. The classical maximum likelihood approach cannot be used for these models since the corresponding masses cannot be expressed in a simple closed form. This paper studies a maximum pairwise likelihood approach to estimate the parameters of multivariate mixed Poisson models when the mixing distribution is a multivariate Gamma distribution. The consistency and asymptotic normality of this estimator are derived. Simulations conducted on synthetic data illustrate these results and show that the proposed estimator outperforms classical estimators based on the method of moments. An application to change detection in low-flux images is also investigated

Asymptotic regime for impropriety tests of complex random vectors

Impropriety testing for complex-valued vector has been considered lately due to potential applications ranging from digital communications to complex media imaging. This paper provides new results for such tests in the asymptotic regime, i.e. when the vector dimension and sample size grow commensurately to infinity. The studied tests are based on invariant statistics named impropriety coefficients. Limiting distributions for these statistics are derived, together with those of the Generalized Likelihood Ratio Test (GLRT) and Roy's test, in the Gaussian case. This characterization in the asymptotic regime allows also to identify a phase transition in Roy's test with potential application in detection of complex-valued low-rank subspace corrupted by proper noise in large datasets. Simulations illustrate the accuracy of the proposed asymptotic approximations.Comment: 11 pages, 8 figures, submitted to IEEE TS

Bivariate Gamma Distributions for Image Registration and Change Detection

This paper evaluates the potential interest of using bivariate gamma distributions for image registration and change detection. The first part of this paper studies estimators for the parameters of bivariate gamma distributions based on the maximum likelihood principle and the method of moments. The performance of both methods are compared in terms of estimated mean square errors and theoretical asymptotic variances. The mutual information is a classical similarity measure which can be used for image registration or change detection. The second part of the paper studies some properties of the mutual information for bivariate Gamma distributions. Image registration and change detection techniques based on bivariate gamma distributions are finally investigated. Simulation results conducted on synthetic and real data are very encouraging. Bivariate gamma distributions are good candidates allowing us to develop new image registration algorithms and new change detectors

Estimating the polarization degree of polarimetric images in coherent illumination using maximum likelihood methods

This paper addresses the problem of estimating the polarization degree of polarimetric images in coherent illumination. It has been recently shown that the degree of polarization associated to polarimetric images can be estimated by the method of moments applied to two or four images assuming fully developed speckle. This paper shows that the estimation can also be conducted by using maximum likelihood methods. The maximum likelihood estimators of the polarization degree are derived from the joint distribution of the image intensities. We show that the joint distribution of polarimetric images is a multivariate gamma distribution whose marginals are univariate, bivariate or trivariate gamma distributions. This property is used to derive maximum likelihood estimators of the polarization degree using two, three or four images. The proposed estimators provide better performance that the estimators of moments. These results are illustrated by estimations conducted on synthetic and real images

von Mises-Fisher approximation of multiple scattering process on the hypersphere

International audienceThis paper presents a ''method of moments'' estimation technique for the study of multiple scattering on the hypersphere. The proposed model is similar to a compound Poisson process evolving on a special manifold: the unit hypersphere. The presented work makes use of an approximation result for multiply convolved von Mises-Fisher distributions on hyperspheres. Comparison with other approximations show the accuracy of the proposed model to provide estimators for the mean free path and concentration parameters when studying a multiple scattering process. Such a process is classically used to model the propagation of waves or particules in random media

Lois Gamma multivariées pour le traitement d'images radar

Dans de nombreux systèmes d'imagerie, et notamment dans des systèmes d'imagerie active tels que le radar, l'amplitude du front de l'onde étudiée est classiquement modélisée par une loi gaussienne complexe. Les intensités mesurées correspondent alors au module au carré de lois gaussiennes complexes. L'estimation des paramètres, appliquée à des problèmes de détection, nécessite de connaître alors précisément les statistiques des intensités reçues. L'objet de cette thèse consiste à étudier des extensions multivariées des lois paramétriques, telles que les lois Gamma, rencontrées dans de tels systèmes d'imagerie. Cette modélisation multivariée permet, en effet, de tenir compte des dépendances statistiques entre des images d'une même scène acquises à des dates différentes et/ou par des capteurs différents. C'est pourquoi les familles de lois multivariées étudiées s'avèrent particulièrement utiles pour résoudre de nombreux problèmes d'estimation et de détection rencontrés en traitement de l'image, telles que la détection de changements temporels ou l'analyse polarimétrique d'une scène. ABSTRACT : The wavefront amplitude of many optical systems can be modeled as a sum of complex components distributed according to Gaussian distributions. In particular, this is the case for active imaging sytems such as radar systems. The resulting intensity measurements are the sum of the squared modulus of these complex Gaussian components. Parameter estimation and detection problems require to determine accurately the statistical properties of the collected intensities. The subject of this thesis consists of studying families of multivariate gamma based distributions useful to solve estimation and detection problems in different image processing applications. Multivariate extensions of the uni-dimensional gamma distribution make possible to model the correlation between images of a same scene acquired at different times and/or by different sensors. Therefore, these distributions are interesting for parameter estimation and detection in many image processing applications, such as in change detection problems or in polarimetric analysis

Multi-Branch Hidden Semi-Markov Modeling for RUL Prognosis

International audienceDeterioration modeling and remaining useful life (RUL) estimation of equipment are key enabling tasks for the implementation of a predictive maintenance (PM) policy, which plays nowadays an important role for maintaining engineering systems. Hidden Markov Models (HMM) have been used as an efficient tool for modeling the deterioration mechanisms as well as for estimating the RUL of monitored equipment. However, due to some assumptions not always justified in practice, the applications of HMM on real-life problems are still very limited. To tackle this issue and to relax some of these unrealistic assumptions, this paper proposes a multi-branch Hidden semi-Markov modeling (MB-HSMM) framework. The proposed deterioration model comprises several different branches, each one being itself an HSMM. The proposed model offers thus the capacity to 1) explicitly model the sojourn time in the different states and 2) take into account multiple co-existing and competing deterioration modes, even within a single component. A diagnosis and RUL prognosis methodology based on the MB-HSMM model is also proposed. Thanks to its multiple branches property, the MB-HSMM model makes it possible not only to assess the current health status of the component but also to detect the actual deterioration mechanism. Based on the diagnostic results, the component RUL can then be calculated. The performance of the proposed model and prognosis method is evaluated through a numerical study. A Fatigue Crack Growth (FCG) model based on the Paris-Erdogan law is used to simulate deterioration data of a bearing under different operation conditions. The results show that the proposed MB-HSMM gives a very promising performance in deterioration mode detection as well as in the RUL estimation, especially in the case where these deterioration modes exhibit very different dynamics