## About

144

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Introduction

I received the degree of Electrical Engineer in 1997, the Ph.D. degree in Signal Processing from the Institut National Polytechnique de Grenoble (INPG) in 2001 and the HdR degree from ENS Cachan in 2011. I was Associate Professor of Université Paris X in the SATIE Lab from 2002 to 2010. I am currently professor of Université de Savoie in the LISTIC Lab. My research interests are in estimation and detection theory with applications to array processing and radar/sonar.

## Publications

Publications (144)

This paper proposes new algorithms for the metric learning problem. We start by noticing that several classical metric learning formulations from the literature can be viewed as modified covariance matrix estimation problems. Leveraging this point of view, a general approach, called Robust Geometric Metric Learning (RGML), is then studied. This met...

This paper tackles the problem of robust covariance matrix estimation when the data is incomplete. Classical statistical estimation methodologies are usually built upon the Gaussian assumption, whereas existing robust estimation ones assume unstructured signal models. The former can be inaccurate in real-world data sets in which heterogeneity cause...

Cyclonic fields are violent atmospheric disturbances associated with swirling winds. These quasi-stochastic fields are the cause of many natural disasters, which motivate early detection methods as well as time monitoring of changing conditions. This chapter discusses some methods for time monitoring and prediction of cyclonic fields. The analysis...

Change detection (CD) for remotely sensed images of the Earth has been a popular subject of study in the past decades. With the increase in the number of spatial missions with embedded synthetic aperture radar (SAR) sensors, the amount of readily available observations has now reached the "big data" era. This chapter introduces several families of...

This paper studies a statistical model for heteroscedastic (i.e., power fluctuating) signals embedded in white Gaussian noise. Using the Riemannian geometry theory, we propose an unified approach to tackle several problems related to this model. The first axis of contribution concerns parameters (signal subspace and power factors) estimation, for w...

The information geometry of the zero-mean t-distribution with Kronecker-product structured covariance matrix is derived. In particular, we obtain the Fisher information metric which shows that this geometry is identifiable to a product manifold of S ++ p (positive definite symmetric matrices) and sS ++ p (positive definite symmetric matrices with u...

This paper tackles the problem of robust covariance matrix estimation when the data is incomplete. Classical statistical estimation methodologies are usually built upon the Gaussian assumption, whereas existing robust estimation ones assume unstructured signal models. The former can be inaccurate in real-world data sets in which heterogeneity cause...

In this paper, robust mean and covariance matrix estimation are considered in the context of mixed-effects models. Such models are widely used to analyze repeated measures data which arise in several signal processing applications that need to incorporate possible individual variations within a common behavior of individuals. In this context, most...

In this paper, we propose a new estimator of the covariance matrix parameters when observations follow a mixture of a deterministic Compound-Gaussian (CG) and a white Gaussian noise. In particular, the covariance matrix of the CG contribution is assumed to be expressed as the Kronecker product of two low-rank matrices, which is a structure often in...

This paper proposes an original Riemmanian geometry for low-rank structured elliptical models, i.e., when samples are elliptically distributed with a covariance matrix that has a low-rank plus identity structure. The considered geometry is the one induced by the product of the Stiefel manifold and the manifold of Hermitian positive definite matrice...

Tutorial at IEEE Radar Conference 2020

Tutorial at IEEE Radar Conference 2020

The blind source separation problem is considered, more specifically the approach based on non-stationarity and coloration. In both cases, sources are usually assumed to be Gaus-sian. In this paper, we extend previous works in order to handle sources drawn from the multivariate Student t-distribution. After studying the data model in this case, a n...

A new Riemannian geometry for the zero-mean Compound Gaussian distribution with deterministic textures is proposed. In particular, the Fisher information metric (up to a factor) is obtained, along with corresponding geodesics and distance function. This new geometry is applied on a change detection problem on Multivariate Image Times Series: a recu...

This paper derives a new change detector for multivariate Synthetic Aperture Radar image time series. Classical statistical change detection methodologies based on covariance matrix analysis are usually built upon the Gaussian assumption, as well as an unstructured signal model. Both of these hypotheses may be inaccurate for high-dimension/resoluti...

A new Riemannian geometry for the Compound Gaussian distribution is proposed. In particular, the Fisher information metric is obtained, along with corresponding geodesics and distance function. This new geometry is applied on a change detection problem on Multivariate Image Times Series: a recursive approach based on Riemannian optimization is deve...

This paper proposes an original Riemmanian geometry for low-rank structured elliptical models, i.e., when samples are elliptically distributed with a covariance matrix that has a low-rank plus identity structure. The considered geometry is the one induced by the product of the Stiefel manifold and the manifold of Hermitian positive definite matrice...

This paper considers the problem of detecting changes in multivariate Synthetic Aperture Radar image time series. Classical methodologies based on covariance matrix analysis are usually built upon the Gaussian assumption, as well as an unstructured signal model. Both of these hypotheses may be inaccurate for high-dimension/resolution images, where...

Ce papier considère la détection de changements dans une série temporelle d'images multivariées obtenues par radar à synthèse d'ouverture. Dans ce cadre les méthodologies classiques modélisent les données par une distribution gaussienne à moyenne nulle et une covariance non structurée. Ces deux hypothèses montrent leur limite lorsque les données so...

Robust scatter matrix estimators are often obtained up to a scaling factor. Since most of the adaptive processes are invariant to this scaling ambiguity, we are mostly interested in estimating a normalized scatter matrix. In the context of complex elliptical symmetric distributions, and the framework of [1], we propose to develop the intrinsic Cram...

This paper considers the problem of detecting changes in mul-tivariate Synthetic Aperture Radar image time series. Classical methodologies based on covariance matrix analysis are usually built upon the Gaussian assumption, as well as an unstructured signal model. Both of these hypotheses may be inaccurate for high-dimension/resolution images, where...

This paper proposes a new approximation of the theoretical Signal to Interference plus Noise Ratio (SINR) loss of the Low-Rank (LR) adaptive filter built on the eigenvalue decomposition of the sample covariance matrix. This new result is based on an analysis in the large dimensional regime, i.e. when the size and the number of data tend to infinity...

This paper introduces an improved Low Rank Adaptive Normalized Matched Filter (LR-ANMF) detector in a high dimensional (HD) context where the observation dimension is large and of the same order of magnitude than the sample size. To that end, the statistical analysis of the LR-ANMF, in a context where the target signal is disturbed by a spatially c...

A growing problem in the remote sensing community concerns the estimation of change-points in a time series of Synthetic Aperture Radar (SAR) images. Although the methodologies of change-point estimation have already been investigated in the literature, there are, to the best of our knowledge, no study on the expected performance for the estimation...

Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to largely outperform the sample covariance matrix estimate and to compete with state-of-the-art methods, while at...

When a possible target is embedded in a Low Rank (LR) Gaussian clutter (which is contained in a low dimensional subspace) plus a white Gaussian noise, the detection process can be performed by applying the Low-Rank Adaptive Normalized Matched Filter (LR-ANMF) which is a function of the estimated projector. In a recent work, we derived an approximat...

This paper explores the problem of change detection in time series of heterogeneous multivariate synthetic aperture radar images. Classical change detection schemes have modelled the data as a realisation of Gaussian random vectors and have derived statistical tests under this assumption. However, when considering high-resolution images, the hetero...

High resolution in synthetic aperture radar (SAR) leads to new physical characterizations of scatterers which are anisotropic and dispersive. These behaviors present an interesting source of diversity for target detection schemes. Unfortunately, such characteristics have been integrated and have been naturally lost in monovariate single-look SAR im...

Scatter matrix and its normalized counterpart, referred to as shape matrix, are key parameters in multivariate statistical signal processing, as they generalize the concept of covariance matrix in the widely used Complex Elliptically Symmetric distributions. Following the framework of [1], intrinsic Cramor-Rao bounds are derived for the problem of...

We consider the classical radar problem of detecting a target in Gaussian noise with unknown covariance matrix, based on multiple primary data and a set of secondary data containing noise only. The most celebrated approach to this problem is Kelly's generalized likelihood ratio test (GLRT), derived under the hypothesis of deterministic target ampli...

In this paper, we study the problem of detecting and estimating change-points in a time series of multivariate images. We extend existent works to take into account the heterogeneity of the dataset on a spatial neighborhood. The classic complex Gaussian assumption of the data is replaced by a complex elliptically symmetric assumption. Then robust s...

In this paper, we propose new detectors for Change Detection between two multivariate images. The data is supposed to follow a Compound Gaussian distribution. By using Likelihood Ratio Test (LRT) and Generalised LRT (GLRT) approaches, we derive our detectors. The CFAR behaviour has been studied and the simulations show that they outperform the clas...

In this paper, we propose new detectors for Change Detection between two multivariate images. The data is supposed to follow a Compound Gaussian distribution. By using Likelihood Ratio Test (LRT) and Generalised LRT (GLRT) approaches, we derive our detectors. The CFAR behaviour has been studied and the simulations show that they outperform the clas...

We develop in this paper a new adaptive LR filter for MIMO-STAP application based on a tensorial modelling of the data. This filter is based on an extension of the HOSVD (which is also one possible extension of SVD to the tensor case), called AU-HOSVD, which allows to consider the combinations of dimensions. This property is necessary to keep the a...

Dans cette communication, nous proposons une expression de la Borne de Cramér-Rao (BCR) intrinsèque concernant la matrice de covariance pour des données issues d'une distribution elliptique complexe générale. Par rapport aux travaux récents sur ce thème, nous nous appuyons sur la propriété géométrique des matrices de covariance d'appartenir à une v...

Nous proposons, dans ce papier, une nouvelle méthodologie pour la Détection de Changement entre deux images SAR monovarié. Des outils d'analyse Temps-Fréquence Linéaire sont utilisés pour obtenir une diversité spectrale et angulaire. Cette diversité est utilisée dans uneprobì eme de détection sur vecteurs multivariés et le détecteur obtenu affiche...

Parmi les estimateurs de matrice de covariance, l'estimateur de Tyler régularisé offre des performances constantes quelle que soit la distribution statistique des données, tout en étant robuste à la présence de données aberrantes. Cependant, la sélection de la valeur du paramètre de régularisation dépend fortement de l'application ciblée et de la c...

Détection de changement pour des images SAR très haute résolution

In this paper, we propose a novel methodology for Change Detection between two monovariate complex SAR images. Linear Time-Frequency tools are used in order to recover a spectral and angular diversity of the scatterers present in the scene. This diversity is used in bi-date change detection framework to develop a detector, whose performances are be...

Usually, in radar imaging, the scatterers are supposed to respond the same way regardless of the angle from which they are viewed and have the same properties within the emitted spectral bandwidth. Nevertheless, new capacities in SAR imaging (large bandwidth, large angular extent) make this assumption obsolete. An original application of the Linear...

Regularized Tyler Estimator's (RTE) have raised attention over the past years due to their attractive performance over a wide range of noise distributions and their natural robustness to outliers. Developing adaptive methods for the selection of the regularisation parameter α is currently an active topic of research. Indeed, the bias-performance co...

This paper addresses the problem of robust covariance matrix (CM) estimation in the context of a disturbance composed of a low rank (LR) heterogeneous clutter plus an additive white Gaussian noise. The LR clutter is modeled by a spherically invariant random vector with assumed high clutter-to-noise ratio. In such a context, adaptive process should...

In this paper, we propose to derive an approximate theoretical
distribution under the null hypothesis of the Low-Rank Adaptive
Normalized Matched Filter (LR-ANMF). This detector is used to detect a
target when the disturbance is composed of a Low-Rank Gaussian contribution
(called clutter) and an Additive White Gaussian Noise (AWGN).
In the LR-ANMF...

Detection of buried objects such as pipes using a Ground Penetrating Radar (GPR) is intricate for three main reasons. First, noise is important in the resulting image because of the presence of several rocks and/or layers in the ground, highly influencing the Probability of False Alarm (PFA) level. Also, wave speed and object responses are unknown...

The Ground Penetrating Radar (GPR) consists in an electromagnetic signal which is transmitted at different positions through the ground in order to obtain an image of the subsoil. In particular, the GPR is used to detect buried objects like pipes. Their detection and localisation are intricate for three main reasons. First, the noise is important i...

In this paper, we derive the theoretical performance of a Tensor MUSIC algorithm based on the Higher Order Singular Value Decomposition (HOSVD), that was previously developed to estimate the Direction Of Arrival (DOA) and the polarization parameters of polarized sources. The derivation of this result is done via a perturbation analysis and allows t...

An original estimator of the orthogonal projector onto the signal subspace is proposed. This estimator is derived as the maximum likelihood estimator for a model of sources plus orthogonal outliers, both with varying power (modeled by Compound Gaussians process), embedded in a white Gaussian noise. Validity and interest — in terms of performance an...

Ce papier se place dans le cadre du filtrage d'un vecteur d'observation composé d'un signal d'intérêt corrompu par un bruit additif rang faible gaussien et un bruit blanc gaussien. Dans ce cadre, au lieu d'utiliser l'inverse de la matrice de covariance, on utilise un projecteur. Le signal filtré n'étant alors pas consistant en régime de grandes dim...

Nous considérons le problème d'estimation de la matrice de covariance (CM) d'un bruit composé d'un fouillis hétérogène de rang faible plus un bruit blanc Gaussien (BBG). Le fouillis est modélisé comme un SIRV ayant a fort rapport "fouillis à bruit" (dénoté CNR). Nous proposons dans ce papier un algorithme générique permettant d'obtenir des estimate...