MERIAUX Bruno - Publications

Journal Papers

B. Mériaux, C. Ren, A. Breloy, M.N. El Korso and P. Forster, "Matched and Mismatched Estimation of Kronecker Product of Linearly Structured Scatter Matrices under Elliptical Distributions", in IEEE Transactions on Signal Processing (2020) (pdf)

Abstract: 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 also exhibit an additional linear structure. Taking this prior knowledge into account during the estimation process drastically reduces the amount of unknown parameters, and then improves the estimation accuracy. On the other hand, the broad class of complex elliptically symmetric distributions, as well as the related complex angular elliptical distribution, are particularly suited to model heavy-tailed multivariate data. In this context, we first establish novel robust estimators of scatter and shape matrices (both related to a covariance matrix), having a Kronecker product structure with linearly structured Kronecker factors. Then, we conduct a theoretical analysis of their asymptotic performance (i.e., consistency, asymptotic distribution and efficiency), in matched and mismatched scenarios, i.e., when misspecifications between the true and assumed models occur. Finally, numerical results illustrate the theoretical analysis and assess the usefulness of the proposed estimators.

B. Mériaux, C. Ren, M.N. El Korso, A. Breloy and P. Forster, "Robust Estimation of Structured Scatter Matrices in (Mis)matched Models", in Elsevier Signal Processing (2019), vol 165, pp. 163-174 (pdf)

Abstract: 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. In this paper, we consider the estimation of structured scatter matrix for complex elliptically distributed observations, where the assumed model can differ from the actual distribution of the observations. Specifically, we tackle this problem, in a mismatched framework, by proposing a novel estimator, named StructurEd ScAtter Matrix Estimator (SESAME), which is based on a two-step estimation procedure. We conduct theoretical analysis on the unbiasedness and the asymptotic efficiency and Gaussianity of SESAME. In addition, we derive a recursive estimation procedure that iteratively applies the SESAME method, called Recursive-SESAME (R-SESAME), reaching with improved performance at lower sample support the (Mismatched) Cramér-Rao Bound. Furthermore, we show that some special cases of the proposed method allow to retrieve preexisting methods. Finally, numerical results corroborate the theoretical analysis and assess the usefulness of the proposed algorithms.

B. Mériaux, C. Ren, M.N. El Korso, A. Breloy and P. Forster, "Asymptotic Performance of Complex M-estimators for Multivariate Location and Scatter Estimation", in IEEE Signal Processing Letters (2019), vol. 26, no. 2, pp. 367-371 (pdf)

Abstract: 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 the seventies. Their extension to the complex case has drawn recent interest. In this letter, we derive the asymptotic performance of complex M-estimators for multivariate location and scatter matrix estimation.

B. Mériaux, X. Zhang, M.N. El Korso and M. Pesavento, "Iterative Marginal Maximum Likelihood DOD and DOA Estimation for MIMO Radar in the Presence of SIRP Clutter", in Elsevier Signal Processing (2019), vol 155, pp. 384-390 (pdf)

Abstract: The spherically invariant random process (SIRP) clutter model is commonly used in scenarios where the radar clutter cannot be correctly modeled as a Gaussian process. In this short communication, we devise a novel Maximum-Likelihood (ML)-based iterative estimator for direction-of-departure and direction-of-arrival estimation in the Multiple-input multiple-output (MIMO) radar context in the presence of SIRP clutter. The proposed estimator employs a stepwise numerical concentration approach w.r.t. the objective function related to the marginal likelihood of the observation data. Our estimator leads to superior performance, as our simulations show, w.r.t. to the existing likelihood based methods, namely, the conventional, the conditional and the joint likelihood based estimators, and w.r.t. the robust subspace decomposition based methods. Finally, interconnections and comparison between the Iterative Marginal ML Estimator (IMMLE), Iterative Joint ML Estimator (IJMLE) and Iterative Conditional ML Estimator (ICdMLE) are provided.

International Conference Papers

B. Mériaux, C. Ren, A. Breloy, M.N. El Korso and P. Forster, "Efficient Estimation of Kronecker Product of Linear Structured Scatter Matrices under t-distribution", in Proc. of 28th European Signal Processing Conference (EUSIPCO 2020), Amsterdam, NETHERLANDS (pdf)

Abstract: This paper addresses structured scatter matrix estimation within the non convex set of Kronecker product structure. The latter model usually involves two matrices, which can be themselves linearly constrained, and arises in many applications, such as MIMO communication, MEG/EEG data analysis. Taking this prior knowledge into account generally improves estimation accuracy. In the framework of robust estimation, the t-distribution is particularly suited to model heavy-tailed data. In this context, we introduce an estimator of the scatter matrix, having a Kronecker product structure and potential linear structured factors. In addition, we show that the proposed method yields a consistent and efficient estimate.

B. Mériaux, A. Breloy, C. Ren, M.N. El Korso and P. Forster, "Modified Sparse Subspace Clustering for Radar Detection in Non-stationary Clutter", in Proc. of IEEE 8th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP 2019), Guadeloupe, FRANCE (pdf)

Abstract: Detecting targets embedded in a noisy environment is an important topic in adaptive array processing. In the traditional statistical framework, this problem is addressed through a binary hypothesis test, which usually requires the estimation of side parameters from secondary data. The latter are assumed to be homogeneous and target-free, which is in practice questionable. Indeed, secondary data are usually corrupted by radar clutters and/or jammers which can be non-stationary and locally low rank. Fortunately, the latter behaviors can be well acknowledged by a union-of-subspaces model. In this work, we propose a modified subspace clustering model which can be solved using convex optimization algorithms. In the context of multiple sparse target detection and localization, a comparison is performed with various robust detection methods exhibiting advantages and drawbacks of the proposed one.

B. Mériaux, C. Ren, A. Breloy, M.N. El Korso, P. Forster and J.-P. Ovarlez, "On the Recursions of Robust COMET Algorithm for Convexly Structured Shape Matrix", in Proc. of 27th European Signal Processing Conference (EUSIPCO 2019), A Coruña, SPAIN, pp. 1-5 (pdf)

Abstract: This paper addresses robust estimation of structured shape (normalized covariance) matrices. Shape matrices most often own a particular structure depending on the application of interest and taking this structure into account improves estimation accuracy. In the framework of robust estimation, we introduce a recursive robust shape matrix estimation technique based on Tyler's M-estimate for convexly structured shape matrices. We prove that the proposed estimator is consistent, asymptotically efficient and Gaussian distributed and we notice that it reaches its asymptotic regime faster as the number of recursions increases. Finally, in the particular wide spreaded case of Hermitian persymmetric structure, we study the convergence of the recursions of the proposed algorithm.

B. Mériaux, C. Ren, M.N. El Korso, A. Breloy and P. Forster, "Efficient Estimation of Scatter Matrix with Convex Structure under t-distribution", in Proc. of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2018), Calgary, CANADA, pp. 4474-4478 (pdf)

Abstract: This paper addresses structured covariance matrix estimation under t-distribution. Covariance matrices frequently reveal a particular structure due to the considered application and taking into account this structure usually improves estimation accuracy. In the framework of robust estimation, the t-distribution is particularly suited to describe heavy-tailed observation. In this context, we propose an efficient estimation procedure for covariance matrices with convex structure under t-distribution. Numerical examples for Hermitian Toeplitz structure corroborate the theoretical analysis.

B. Mériaux, C. Ren, M.N. El Korso, A. Breloy and P. Forster, "Robust-COMET for Covariance Estimation in Convex Structures: Algorithm and Statistical Properties ", in Proc. of IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP 2017), Curaçao, NETHERLANDS, pp. 1-5 (pdf)

Abstract: This paper deals with structured covariance matrix estimation in a robust statistical framework. Covariance matrices often exhibit a particular structure related to the application of interest and taking this structure into account increases estimation accuracy. Within the framework of robust estimation, the class of circular Complex Elliptically Symmetric (CES) distributions is particularly interesting to handle impulsive and spiky data. Normalized CES random vectors are known to share a common Complex Angular Elliptical distribution. In this context, we propose a Robust Covariance Matrix Estimation Technique (RCOMET) based on Tyler's estimate and COMET criterion for convexly structured matrices. We prove that the proposed estimator is consistent and asymptotically efficient while computationally attractive. Numerical results support the theoretical analysis in a particular application for Hermitian Toeplitz structure.

National Conference Papers

B. Mériaux, C. Ren, A. Breloy, M.N. El Korso, P. Forster et J.-P. Ovarlez, "Une version récursive de RCOMET pour l’estimation robuste de matrices de forme à structure convexe", GRETSI 2019, Lille, FRANCE (pdf)

Résumé : Ce papier porte sur l’estimation robuste de matrices de forme (covariance normalisée) structurées. Dans un contexte d’estimation robuste, nous introduisons un estimateur robuste et récursif de matrice de forme basé sur l’estimateur de Tyler. Nous prouvons que cet estimateur est consistant, asymptotiquement efficace et gaussien. Par ailleurs, nous constatons qu’il atteint son régime asymptotique d’autant plus rapidement que le nombre d’itérations augmente. Finalement, nous étudions la convergence des récursions pour la structure persymétrique hermitienne.

B. Mériaux, C. Ren, M.N. El Korso, A. Breloy et P. Forster, "Estimation robuste de matrices de dispersion structurées pour des modèles bien/mal spécifiés", GRETSI 2019, Lille, FRANCE (pdf)

Résumé : Dans la plupart des méthodes récentes en traitement du signal, les données sont modélisées par des distributions non gaussiennes, dont la matrice de covariance possède une structure particulière. Prendre ces propriétés en compte dans le processus d’estimation améliore nettement la qualité des estimées. Dans ce papier, nous considérons l’estimation de matrices de dispersion structurées, où le modèle supposé peut différer du vrai modèle des données. Plus précisément, nous proposons une nouvelle classe d’estimateurs dénommée StructurEd ScAtter Matrix Estimator (SESAME) dans un contexte de modèles mal spécifiés. Nous menons aussi une analyse théorique de leurs performances asymptotiques.