Clutter Subspace Estimation in Low Rank Heterogeneous Noise Context

International audienceThis 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 training vectors than classical methods to reach equivalent performance. Unlike classical adaptive processes, which are based on an estimate of the noise Covariance Matrix (CM), the LR processes are based on a CSP estimate. This CSP estimate is usually derived from a Singular Value Decomposition (SVD) of the CM estimate. However, no Maximum Likelihood Estimator (MLE) of the CM has been derived for the considered disturbance model. In this paper, we introduce the fixed point equation that MLE of the CSP satisfies for a disturbance composed of a LR-SIRV clutter plus a zero mean WGN. A recursive algorithm is proposed to compute this solution. Numerical simulations validate the introduced estimator and illustrate its interest compared to the current state of art

Through the Wall Radar Imaging via Kronecker-structured Huber-type RPCA

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 of the wall and targets via low rank plus sparse matrix decomposition and obtain better performances. In this paper, we reformulate this precisely via a RPCA-type problem, where the sparse vector appears in a Kronecker product. We extend this approach by adding a robust distance with flexible structure to handle heterogeneous noise and outliers, which may appear in TWRI measurements. The resolution is achieved via the Alternating Direction Method of Multipliers (ADMM) and variable splitting to decouple the constraints. The removal of the front wall is achieved via a closed-form proximal evaluation and the recovery of targets is possible via a tailored Majorization-Minimization (MM) step. The analysis and validation of our method is carried out using Finite-Difference Time-Domain (FDTD) simulated data, which show the advantage of our method in detection performance over complex scenarios

CFAR property and robustness of the lowrank adaptive normalized matched filters detectors in low rank compound gaussian context

International audienceIn 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 context, adaptive LR schemes have been shown to require less secondary data to reach equivalent performances as classical ones. The LR approximation consists on cancelling the clutter rather than whitening the whole noise. The main problem is then the estimation of the clutter subspace instead of the noise covariance matrix itself. Maximum Likelihood estimators (MLE), under different hypothesis [1][2][3], of the clutter subspace have been recently proposed for a noise composed of a LR Compound Gaussian (CG) clutter plus a white Gaussian Noise (WGN). This paper focuses on the performances of the LR Adaptive Normalized Matched Filter (LR-ANMF) detector based on these different clutter subspace estimators. Numerical simulations illustrate its CFAR property and robustness to outliers

Numerical performances of low rank stap based on different heterogeneous clutter subspace estimators

International audienceSpace 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 reach equivalent performance. Unlike the classical filter which is based on the Covariance Matrix (CM) of the noise, the LR filter is based on the clutter subspace projector, which is usually derived from a Singular Value Decomposition (SVD) of a noise CM estimate. Regarding to the considered model of LR-CG plus WGN, recent results are providing both direct estimators of the clutter subspace [1][2] and an exact MLE of the noise CM [3]. To promote the use of these new estimation methods, this paper proposes to apply them to realistic STAP simulations

Online Change Detection in SAR Time-Series with Kronecker Product Structured Scaled Gaussian Models

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 structured covariance matrix under the null hypothesis, which is performed through a recursive (natural) Riemannian gradient descent. This approach exhibits a practical interest compared to the corresponding offline version, as its computational cost remains constant for each new image added in the time series. Simulations show that the proposed recursive estimators reach the Intrinsic Cram\'er-Rao bound. The interest of the proposed online CD approach is demonstrated on both simulated and real data

Algorithmes d’Estimation et de Détection en Contexte Hétérogène Rang Faible

One purpose of array processing is the detection and location of a target in a noisy environment. In most cases (as RADAR or active SONAR), statistical properties of the noise, especially its covariance matrix, have to be estimated using i.i.d. samples. Within this context, several hypotheses are usually made: Gaussian distribution, training data containing only noise, perfect hardware. Nevertheless, it is well known that a Gaussian distribution doesn’t provide a good empirical fit to RADAR clutter data. That’s why noise is now modeled by elliptical process, mainly Spherically Invariant Random Vectors (SIRV). In this new context, the use of the SCM (Sample Covariance Matrix), a classical estimate of the covariance matrix, leads to a loss of performances of detectors/estimators. More efficient estimators have been developed, such as the Fixed Point Estimator and M-estimators.If the noise is modeled as a low-rank clutter plus white Gaussian noise, the total covariance matrix is structured as low rank plus identity. This information can be used in the estimation process to reduce the number of samples required to reach acceptable performance. Moreover, it is possible to estimate the basis vectors of the clutter-plus-noise orthogonal subspace rather than the total covariance matrix of the clutter, which requires less data and is more robust to outliers. The orthogonal projection to the clutter plus noise subspace is usually calculated from an estimatd of the covariance matrix. Nevertheless, the state of art does not provide estimators that are both robust to various distributions and low rank structured.In this Thesis, we therefore develop new estimators that are fitting the considered context, to fill this gap. The contributions are following three axes :- We present a precise statistical model : low rank heterogeneous sources embedded in a white Gaussian noise.We express the maximum likelihood estimator for this context.Since this estimator has no closed form, we develop several algorithms to reach it effitiently.- For the considered context, we develop direct clutter subspace estimators that are not requiring an intermediate Covariance Matrix estimate.- We study the performances of the proposed methods on a Space Time Adaptive Processing for airborne radar application. Tests are performed on both synthetic and real data.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 pour les traitements adaptatifs RADAR, il fautestimer dans un premier temps les propriétés statistiques du bruit, plus précisément sa matrice de covariance.Dans ce contexte, on formule généralement l’hypothèse de bruit gaussien. Il est toutefois connuque le bruit en RADAR est de nature impulsive et que l’hypothèse gaussienne est parfois mal adaptée.C’est pourquoi, depuis quelques années, le bruit, et en particulier le fouillis de sol, est modélisé pardes processus couvrant un panel plus large de distributions, notamment les Spherically Invariant RandomVectors (SIRVs). Dans ce nouveau cadre théorique, la Sample Covariance Matrix (SCM) estimantclassiquement la matrice de covariance du bruit entraîne des pertes de performances importantes desdétecteurs/estimateurs. Dans ce contexte non-gaussien, d’autres estimateurs (e.g. les M-estimateurs),mieux adaptés à ces statistiques de bruits impulsifs, ont été développés.Parallèlement, il est connu que le bruit RADAR se décompose sous la forme d’une somme d’unfouillis de rang faible (la réponse de l’environnement) et d’un bruit blanc (le bruit thermique). La matricede covariance totale du bruit a donc une structure de type rang faible plus identité. Cette informationpeut être utilisée dans le processus d’estimation afin de réduire le nombre de données nécessaires. Deplus, il aussi est possible de construire des traitements adaptatifs basés sur un estimateur du projecteurorthogonal au sous espace fouillis, à la place d’un estimateur de la matrice de covariance. Les traitementsadaptatifs basés sur cette approximation nécessitent aussi moins de données secondaires pour atteindredes performances satisfaisantes. On estime classiquement ce projecteur à partir de la décomposition envaleurs singulières d’un estimateur de la matrice de covariance.Néanmoins l’état de l’art ne présente pas d’estimateurs à la fois robustes aux distributions impulsives,et rendant compte de la structure rang faible des données. C’est pourquoi nos travaux se focalisentsur le développement de nouveaux estimateurs (de covariance et de sous espace fouillis) directementadaptés au contexte considéré. Les contributions de cette thèse s’orientent donc autour de trois axes :- Nous présenterons le modèle de sources impulsives ayant une matrice de covariance de rang faiblenoyées dans un bruit blanc gaussien. Ce modèle, fortement justifié dans de nombreuses applications, acependant peu été étudié pour la problématique d’estimation de matrice de covariance. Le maximum devraisemblance de la matrice de covariance pour ce contexte n’ayant pas une forme analytique directe,nous développerons différents algorithmes pour l’atteindre efficacement- Nous développerons de plus nouveaux estimateurs directs de projecteur sur le sous espace fouillis, nenécessitant pas un estimé de la matrice de covariance intermédiaire, adaptés au contexte considéré.- Nous étudierons les performances des estimateurs proposés sur une application de Space Time AdaptativeProcessing (STAP) pour radar aéroporté, au travers de simulations et de données réelles

Robust estimation of the clutter subspace for a Low Rank heterogeneous noise under high Clutter to Noise Ratio assumption

International audienceIn the context of an heterogeneous disturbance with a Low Rank (LR) structure (called clutter), one may use the LR approximation for filtering and detection process. These methods are based on the projector onto the clutter subspace instead of the noise covariance matrix. In such context, adaptive LR schemes have been shown to require less secondary data to reach equivalent performances as classical ones. The main problem is then the estimation of the clutter subspace instead of the noise covariance matrix itself. Maximum Likelihood estimator (MLE) of the clutter subspace has been recently studied for a noise composed of a LR Spherically Invariant Random Vector (SIRV) plus a white Gaussian Noise (WGN). This paper focuses on environments with a high Clutter to Noise Ratio (CNR). An original MLE of the clutter subspace is proposed in this context. A cross-interpretation of this new result and previous ones is provided. Validity and interest - in terms of performance and robustness - of the different approaches are illustrated through simulation results

Robust Low-rank Change Detection for SAR Image Time Series

International audienceThis 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 the noise can be heterogeneous (non-Gaussian) and where all channels are not always informative (low-rank structure). In this paper, we tackle these two issues by proposing a new detector assuming a robust low-rank model. Analysis of the proposed method on a UAVSAR dataset shows promising results

Studien zur Initiation der O-Mannosylierung in Dystroglykan

1. In dieser Arbeit wurde gezeigt, dass die seltene Modifikation der Protein-OMannosylierung in Säugetieren nicht Sequon-abhängig ist, sondern durch eine Nterminale regulatorische Sequenz kontrolliert wird. Auf einer Serie rekombinanter Glykosylierungssonden, basierend auf kurzen Abschnitten der Muzindomäne des in vivo O-mannosylierten Proteins a-Dystroglykan, wurde eine Modifizierung mit O-Mannosyl-Glykanen abhängig von N-terminalen Peptidregionen beobachtet. Eine Strukturanalyse zeigte die Modifizierung O-mannosylierter Sonden mit sialylierten Glykanen des Muzintyps sowie mit dem O-Mannose-Tetrasaccharid Sia2-3Gal1-4GlcNAc1-2Man-ol an. Es konnte gezeigt werden, dass sich die OMannosyl- Glykane unter anderem auf einem Abschnitt im N-terminalen Bereich der Muzindomäne befinden. Bei Abwesenheit der N-terminalen Sequenzen werden diese O-Mannosylierungsstellen mit Glykanen des Muzintyps modifiziert. Versuche zur O-Glykosylierung in vitro bestätigen, dass synthetische Peptide mit O-Mannosylierungsstellen als Target für die Polypeptid-N-Acetylgalaktosaminyltransferasen dienen, nicht jedoch für die Protein-O-Mannosyltransferasen. Möglicherweise regulatorisch wirkende Sequenzabschnitte des humanen a- Dystroglykans führten bei der Fusion mit einem muzintyp-glykosylierten Protein (MUC1) jedoch nicht zu einer Veränderung dessen Glykosylierungsprofils. 2. In D. melanogaster ist eine Protein-O-Mannosylierung trotz aktiver Protein-OMannosyltransferasen bisher ebenso unbekannt wie das Glykosylierungsprofil des Drosophila-Dystroglykans. Wir konnten zeigen, dass die isolierte Muzindomäne des Drosophila-Dystroglykans, rekombinant exprimiert in EBNA-293- und C2F3- Zellen, keine Informationen zur O-Mannosylierung trägt sondern mit Glykanen des Muzintyps glykosyliert wird. Der extrazelluläre Abschnitt des Proteins, exprimiert in Schneider 2-Zellen, ist trotz potentieller N-Glykosylierungsstellen ausschließlich O-glykosyliert. Die Glykane sind neben der in D. melanogaster bekannten core1-Struktur aus einem acidischen Trisaccharid der Struktur HexA1- 3Gal-1-3GalNAc-ol sowie möglicherweise nicht-elongierter Mannose zusammengesetzt, wobei die beiden letztgenannten Strukturen zum erstenmal in D. melanogaster nachgewiesen wurden

Riemannian optimization for non-centered mixture of scaled Gaussian distributions

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 negative log- likelihood (NLL). The latter makes the trade-off between a white Gaussian distribution and the NC-MSG. Conditions on the regularization are given so that the existence of a minimum to this problem is guaranteed without assumptions on the samples. Then, the Kullback-Leibler (KL) divergence between two NC-MSG is derived. This divergence enables us to define a minimization problem to compute centers of mass of several NC-MSGs. The proposed Riemannian gradient descent algorithm is leveraged to solve this second minimization problem. Numerical experiments show the good performance and the speed of the Riemannian gradient descent on the two problems. Finally, a Nearest centroid classifier is implemented leveraging the KL divergence and its associated center of mass. Applied on the large scale dataset Breizhcrops, this classifier shows good accuracies as well as robustness to rigid transformations of the test set