Arnaud Breloy

Arnaud Breloy
University Paris Nanterre · LEME

Assistant Professor

About

73
Publications
4,805
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268
Citations

Publications

Publications (73)
Article
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...
Preprint
Full-text available
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...
Preprint
Full-text available
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...
Article
Full-text available
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...
Chapter
Full-text available
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...
Article
Full-text available
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...
Preprint
Full-text available
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...
Conference Paper
Full-text available
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...
Preprint
Full-text available
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...
Article
Full-text available
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...
Article
Full-text available
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...
Article
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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...
Article
Full-text available
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...
Article
Full-text available
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...
Presentation
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Tutorial at IEEE Radar Conference 2020
Article
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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...
Conference Paper
Full-text available
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...
Preprint
Full-text available
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...
Article
Full-text available
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...
Preprint
Full-text available
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...
Article
Full-text available
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...
Article
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...
Article
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...
Article
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...
Conference Paper
Full-text available
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...
Conference Paper
Full-text available
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...
Article
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...
Conference Paper
Full-text available
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...
Article
Full-text available
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...
Article
Full-text available
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...
Article
Full-text available
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...
Preprint
Full-text available
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...
Article
Full-text available
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...
Conference Paper
Full-text available
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...
Conference Paper
Full-text available
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...
Conference Paper
Full-text available
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...
Conference Paper
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...
Article
Full-text available
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...
Conference Paper
This paper addresses the problem of the clutter subspace projector estimation in the context of a disturbance composed of a low rank heterogeneous (Compound Gaussian) clutter and white Gaussian noise. We derive two algorithms based on the block majorization-minimization framework to reach the maximum likelihood estimator of the considered model. Th...
Conference Paper
Full-text available
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...
Conference Paper
Full-text available
This paper presents two different approaches to derive the asymptotic distributions of the robust Adaptive Normalized Matched Filter (ANMF) under both H 0 and H 1 hypotheses. More precisely, the ANMF has originally been derived under the assumption of partially homogenous Gaussian noise, i.e. where the variance is different between the observation...
Thesis
Une des finalités du traitement d’antenne est la détection et la localisation de cibles en milieu bruité. Dans la plupart des cas pratiques, comme par exemple le RADAR ou le SONAR actif, il faut estimer dans un premier temps les propriétés statistiques du bruit, et plus précisément sa matrice de covariance ; on dispose à cette fin de données second...
Conference Paper
Full-text available
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...
Article
Full-text available
This paper addresses the problem of the Clutter Subspace Projector (CSP) estimation in the context of a disturbance composed of a Low Rank (LR) heterogeneous clutter, modeled here by a Spherically Invariant Random Vector (SIRV), plus a white Gaussian noise (WGN). In such context, the corresponding LR adaptive filters and detectors require less trai...
Article
This paper addresses the problem of the clutter subspace projector estimation in the context of a disturbance composed of a low rank heterogeneous (Compound Gaussian) clutter and white Gaussian noise. In such a context, adaptive processing based on an estimated orthogonal projector onto the clutter subspace (instead of an estimated covariance matri...
Conference Paper
Full-text available
Space time Adaptive Processing (STAP) for airborne RADAR fits the context of a disturbance composed of a Low Rank (LR) clutter, here modeled by a Compound Gaussian (CG) process, plus a white Gaussian noise (WGN). In such context, the corresponding LR adaptive filters used to detect a target require less training vectors than classical methods to re...
Conference Paper
Full-text available
In the context of an heterogeneous disturbance with a Low Rank (LR) structure (referred to as clutter), one may use the LR approximation for detection process. Indeed, in such con-text, adaptive LR schemes have been shown to require less secondary data to reach equivalent performances as classical ones. The LR approximation consists on cancelling t...
Conference Paper
Full-text available
In the context of an heterogeneous disturbance with a Low Rank (LR) structure (called clutter), one may use the LR ap-proximation for filtering and detection process. These meth-ods are based on the projector onto the clutter subspace in-stead of the noise covariance matrix. In such context, adaptive LR schemes have been shown to require less secon...