# Arnaud BreloyConservatoire National des Arts et Métiers | CNAM · Centre d'Etudes et De Recherche en Informatique et Communications (CEDRIC)

Arnaud Breloy

Doctor of Engineering

## About

97

Publications

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507

Citations

## Publications

Publications (97)

When dealing with a parametric statistical model, a Riemannian manifold can naturally appear by endowing the parameter space with the Fisher information metric. The geometry induced on the parameters by this metric is then referred to as the Fisher–Rao information geometry. Interestingly, this yields a point of view that allows for leveraging many...

We develop the information geometry of scaled Gaussian distributions for which the covariance matrix exhibits a Kronecker product structure. This model and its geometry are then used to propose an online change detection (CD) algorithm for multivariate image times series (MITS). The proposed approach relies mainly on the online estimation of the st...

This paper presents a new performance bound for estimation problems where the parameter to estimate lies in a Riemannian manifold (a smooth manifold endowed with a Riemannian metric) and follows a given prior distribution. In this setup, the chosen Riemannian metric induces a geometry for the parameter manifold, as well as an intrinsic notion of th...

Graphical models and factor analysis are well-established tools in multivariate statistics. While these models can be both linked to structures exhibited by covariance and precision matrices, they are generally not jointly leveraged within graph learning processes. This paper therefore addresses this issue by proposing a flexible algorithmic framew...

The detection of multiple targets in an enclosed scene, from its outside, is a challenging topic of research addressed by Through-the-Wall Radar Imaging (TWRI). Traditionally, TWRI methods operate in two steps: first the removal of wall clutter then followed by the recovery of targets positions. Recent approaches manage in parallel the processing o...

The detection of multiple targets in an enclosed scene, from its outside, is a challenging topic of research addressed by Through-the-Wall Radar Imaging (TWRI). Traditionally, TWRI methods operate in two steps: first the removal of wall clutter then followed by the recovery of targets positions. Recent approaches manage in parallel the processing o...

This paper proposes an algorithm for phase differences estimation in multi-temporal InSAR. The proposed approach is based on covariance fitting estimation and the majorization-minimization algorithm. Experiments with Sentinel-1 images of Mexico City demonstrate that the proposed approach compares favorably to the state-of-the-art phase linking (i.e...

Phase linking is a prominent methodology to estimate coherence and phase difference in interferometric synthetic-aperture radar. This method is driven by a maximum likelihood estimation approach, which allows to fully exploit all the possible interferograms from a time series. Its performance is, however, known to be affected by the accuracy of the...

This paper studies the statistical model of the non-centered mixture of scaled Gaussian distributions (NC-MSG). Using the Fisher-Rao information geometry associated with this distribution, we derive a Riemannian gradient descent algorithm. This algorithm is leveraged for two minimization problems. The first is the minimization of a regularized nega...

Graphical models and factor analysis are well-established tools in multivariate statistics. While these models can be both linked to structures exhibited by covariance and precision matrices, they are generally not jointly leveraged within graph learning processes. This paper therefore addresses this issue by proposing a flexible algorithmic framew...

This paper studies the statistical model of the non-centered mixture of scaled Gaussian distributions (NC-MSG). Using the Fisher-Rao information geometry associated to this distribution, we derive a Riemannian gradient descent algorithm. This algorithm is leveraged for two minimization problems. The first one is the minimization of a regularized ne...

Cet ouvrage traite des avancées en analyse des séries chronologiques d’images de télédétection par apprentissages statistique, automatique et/ou profond. Il présente un éventail de modèles mathématiques, de méthodes d’extraction d’informations spatio-temporelles et d’applications en observation de la Terre.Détection de changements et analyse des sé...

his 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 GeometricMetric Learning (RGML), is then studied. This metho...

Through-the-wall radar imaging (TWRI) is an on-
going field of research which aims at investigating the inside of
a building from its outside. In the most common setting, it seeks
to detect or monitor stationary targets. Departing from usual
delay-and-sum techniques, sparse recovery problems have been
proposed to solve this detection problem. These...

This paper presents a new algorithm for improving the estimation of interferometric SAR (InSAR) phases in the context of time series and phase linking approach. Based on maximum likelihood estimator of a multivariate Gaussian model, the estimation of the InSAR phases is solved using a Block Coordinate Descent algorithm. Compared to the state-of-the...

Radio interferometers are phased arrays producing high-resolution images from the covariance matrix of measurements. Calibration of such instruments is necessary and is a critical task. This is how the estimation of instrumental errors is usually done thanks to the knowledge of referenced celestial sources. However, the use of high sensitive antenn...

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...

Radio interferometers are phased arrays producing high-resolution images from the covariance matrix of measurements. Calibration of such instruments is necessary and is a critical task. This is how the estimation of instrumental errors is usually done thanks to the knowledge of referenced celestial sources. However, the use of high sensitive antenn...

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...

Covariance matrix tapers have a long history in signal processing and related fields. Examples of applications include autoregressive models (promoting a banded structure) or beamforming (widening the spectral null width associated with an interferer). In this paper, the focus is on high-dimensional setting where the dimension
$p$
is high, while...

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...

Covariance matrix tapers have a long history in signal processing and related fields. Examples of applications include autoregressive models (promoting a banded structure) or beamforming (widening the spectral null width associated with an interferer). In this paper, the focus is on high-dimensional setting where the dimension $p$ is high, while th...

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 a framework for optimizing cost functions of orthonormal basis learning problems, such as principal component analysis (PCA), subspace recovery, orthogonal dictionary learning, etc. The optimization algorithm is derived using the majorization-minimization framework in conjunction with orthogonal projection reformulations to deal...

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...

The estimation of covariance matrices is a core problem in many modern adaptive signal processing applications. For matrix- and array-valued data, e.g., MIMO communication, EEG/MEG (time versus channel), the covariance matrix of vectorized data may belong to the non-convex set of Kronecker product structure. In addition, the Kronecker factors can a...

Tutorial at IEEE Radar Conference 2020

Tutorial at IEEE Radar Conference 2020

Various methods have been proposed to estimate the direction of arrival (DOA) of sources under the assumption of Gaussian noise. This assumption, based on the central limit theorem, has been mainly used because it offers an appropriate model in a homogeneous environment. Nevertheless, under certain conditions, the Gaussian hypothesis cannot fully r...

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...

This paper proposes a framework for optimizing cost functions of orthonormal basis learning problems, such as principal component analysis (PCA), subspace recovery, orthogonal dictionary learning, etc. The optimization algorithm is derived using the majorization-minimization framework in conjunction with orthogonal Procrustes reformulations to deal...

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...

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...

The eigenvalue decomposition (EVD) parameters of the second order statistics are ubiquitous in statistical analysis and signal processing. Notably, the EVD of the
$M$
-estimators of the scatter matrix is a popular choice to perform robust probabilistic PCA or other dimension reduction related applications. Towards the goal of characterizing this...

This paper provides an original asymptotic analysis of robust adaptive detectors performance in the context of non-Gaussian observations. We focus on a single-steering case in homogeneous environment and analyze the properties of different adaptive detectors such as Adaptive (Normalized) Matched Filter (AMF/ANMF), Kelly’s GLRT, and Rao test when an...

In this paper, we consider the problem of low dimensional signal subspace estimation in a Bayesian context. We focus on compound Gaussian signals embedded in white Gaussian noise, which is a realistic modeling for various array processing applications. Following the Bayesian framework, we derive two algorithms to compute the maximum a posteriori (M...

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...

Covariance matrix estimation is a ubiquitous problem in signal processing. In most modern signal processing applications, data are generally modeled by non-Gaussian distributions with covariance matrices exhibiting a particular structure. Taking into account this structure and the non-Gaussian behavior improve drastically the estimation accuracy. I...

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...

Testing the similarity of covariance matrices from groups of observations has been shown to be a relevant approach for change and/or anomaly detection in synthetic aperture radar images. While the term "similarity" usually refers to equality or proportionality, we explore the testing of shared properties in the structure of low rank plus identity c...

The joint estimation of means and scatter matrices is often a core problem in multivariate analysis. In order to overcome robustness issues, such as outliers from Gaussian assumption, M-estimators are now preferred to the traditional sample mean and sample covariance matrix. These estimators are well established and studied in the real case since t...

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...

The eigenvalue decomposition (EVD) parameters of the second order statistics are ubiquitous in statistical analysis and signal processing. Notably, the EVD of robust scatter $M$-estimators is a popular choice to perform robust probabilistic PCA or other dimension reduction related applications. Towards the goal of characterizing the behavior of the...

We consider the problem of signal subspace estimation from a given sample set. We rely on the Bayesian framework developped in [1] to obtain minimum mean square distance (MMSD) estimators, which minimize the expected distance between the true projection matrix UU T and its estimate ÛÛ T. In this work, we extend the estimators of [1] to the context...

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...

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...

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...

The co-centered orthogonal loop and dipole array is commonly used in sources localization using jointly the polarization and spatial diversities. For this type of array, most of the performance analysis studies present in the literature rely on asymptotic regimes. In this paper, we focus on the performance analysis in the non-asymptotic region. Mor...