Fonctions de contraste et cumulants croisés pour la séparation de mélanges convolutifs

Nous considérons le problème de la séparation de mélanges de signaux statistiquement indépendants en contexte convolutif. Notre approche est fondée sur la maximisation de fonctions de contraste. Après un rappel préalable de la définition des fonctions de contraste, nous montrons que dans le cadre des mélanges convolutifs, on peut considérer des contrastes comportant des cumulants croisés. Quatre nouveaux contrastes contenant des cumulants croisés sont donc introduits, l'un d'eux généralise au cas convolutif celui de [1], deux des quatre autres sont intermédiaires entre le contraste de P. Comon [3] et le précédent. Enfin le dernier se révèle spécifique au cas des mélanges convolutifs

Au sujet d'un contraste non symétrique

On considère le problème de la séparation de sources basée sur l'optimisation de critères. Nous proposons une définition des fonctions de contraste plus générale afin de pouvoir considérer des fonctions non symétriques et nous donnons deux nouveaux contrastes. Dans le cas de deux sources, nous déterminons le coefficient de dissymétrie optimal en minimisant l'erreur quadratique moyenne d'estimation. Nous illustrons les résultats au moyen de simulations numériques qui témoignent de l'intérêt qu'il peut y avoir à considérer un contraste non symétrique

Nonnegative 3-way tensor factorization via conjugate gradient with globally optimal stepsize

International audienceThis paper deals with the minimal polyadic decomposition (also known as canonical decomposition or Parafac) of a 3-way array, assuming each entry is positive. In this case, the low-rank approximation problem becomes well-posed. The suggested approach consists of taking into account the nonnegative nature of the loading matrices directly in the problem parameterization. Then, the three gradient components are derived allowing to efficiently implement the decomposition using classical optimization algorithms. In our case, we focus on the conjugate gradient algorithm, well matched to large problems. The good behaviour of the proposed approach is illustrated through computer simulations in the context of data analysis and compared to other existing approaches

Computing the polyadic decomposition of nonnegative third order tensors

International audienceComputing the minimal polyadic decomposition (also often referred to as canonical decomposition, or sometimes Parafac) amounts to finding the global minimum of a coercive polynomial in many variables. In the case of arrays with nonnegative entries, the low-rank approximation problem is well posed. In addition, due to the large dimension of the problem, the decomposition can be rather efficiently calculated with the help of preconditioned nonlinear conjugate gradient algorithms, as subsequently shown, if equipped with an algebraic calculation of the globally optimal stepsize in low dimension. Other algorithms are also studied (gradient and quasi-Newton approaches) for comparisons. Two versions of each algorithm are considered: the Enhanced Line Search version (ELS), and the backtracking version alternating with ELS. Computer simulations are provided and demonstrate the good behavior of these algorithms dedicated to nonnegative arrays, compared to others put forward in the literature. Finally, applications in the context of data analysis illustrate various algorithms. The main advantage of the suggested approach is to explicitly take into account the nonnegative nature of the loading matrices in the problem parameterization, instead of enforcing positive entries by projection. According to the experiments we have run, such an approach also happens to be more robust with respect to possible modeling errors

Computing the nonnegative 3-way tensor factorization using Tikhonov regularization

International audienceThis paper deals with the minimum polyadic decomposition of a nonnegative three-way array. The main advantage of the nonnegativity constraint is that the approximation problem becomes well posed. To tackle this problem, we suggest the use of a cost function including penalty terms built with matrix exponentials. Gradient components are then derived, allowing to efficiently implement the decomposition using classical optimization algorithms. In our case, Alternating Least Squares (ALS) and conjugate gradient algorithms are studied and compared with another existing algorithm, thanks to computer simulations performed in the context of data analysis

Study Of Different Strategies For The Canonical Polyadic Decomposition Of Nonnegative Third Order Tensors With Application To The Separation Of Spectra In 3D Fluorescence Spectroscopy

International audienceIn this communication, the problem of blind source separation in chemical analysis and more precisely in the fluo-rescence spectroscopy framework is addressed. Classically multi-linear Canonical Polyadic (CP or Candecomp/Parafac) decompositions algorithms are used to perform that task. Yet, as the constituent vectors of the loading matrices should be nonnegative since they stand for nonnegative quantities (spectra and concentrations), we focus on NonNegative CP decomposition algorithms (NNCP). In the unconstrained case, two types of trilinear (or triadic) decomposition model have been studied. Here, our aim is to investigate different strategies concerning the choice of models and optimization schemes in the case of a nonnegativity constraint. Computer simulations are performed on synthetic data to illustrate the robustness of the proposed approaches versus overfactoring problems but also the critical importance of the use of regularization terms

Error Analysis of Low-rank Three-Way Tensor Factorization Approach to Blind Source Separation

International audienceIn tensor factorization approaches to blind separation of multidimensional sources, two formulas for calculating the source tensor have emerged. In practice, it is observed that these two schemes exhibit different levels of robustness against perturbations of the factors involved in the tensor model. Motivated by both practical reasons and the will to better figure this out, we present error analyses in source tensor estimation performed by low-rank factorization of three-way tensors. To that aim, computer simulations as well as the analytical calculation of the theoretical error are carried out. The conclusions drawn from these numerical and analytical error analyses are supported by the results obtained thanks to tensor-based blind decomposition of an experimental multispectral image of a skin tumor

Measuring fish activities as additional environmental data during a hydrographic survey with a multi-beam echo sounder

International audienceThe modern multi-beam echo sounders (MBES) are advanced instrumentation for active underwater acoustic surveys that can be boarded on oceanic vessels as well on light crafts. Although their versatility allows scientists to perform various environmental studies, their potential is seldom fully exploited. A single data acquisition cruise is not only able to display the seabed backscatter, but also provide an estimation of the fish activities from an underwater site thanks to water column imagery. This work is aiming at developing some (automatic) signal processing techniques to detect, analyse and classify objects observed in the water column with a focus on fish activities to provide fish accumulation and classification but also some comparative analyses along with the seafloor classification

Un nouvel algorithme de bloc diagonalisation conjointe pour la séparation de sources en mélanges convolutifs

Nous considérons le problème de la séparation aveugle de mélanges convolutifs de sources. Nous proposons un nouvel algorithme de bloc-diagonalisation conjointe d'un ensemble de matrices sous transformation non-orthogonale. Il repose sur l'optimisation algébrique d'un critère de type moindres carrés. L'intérêt majeur d'une telle approche, outre le fait qu'elle soit plus générale, est de rendre facultatif le blanchiment des observations. Des simulations informatiques sont présentées afin d'illustrer l'efficacité de l'approche proposée dans trois cas de figure : lorsque les matrices considérées sont exactement bloc-diagonales puis lorsqu'elles sont progressivement perturbées par un bruit additif Gaussien et enfin dans le contexte de la séparation aveugle de mélanges convolutifs de sources (les matrices considérées sont alors des matrices de covariance estimées)

Joint Maximum Likelihood Sequence Estimation algorithm for decollision of AIS signals in maritime surveillance context

This paper addresses the Joint Maximum-Likelihood Sequence Estimation (JMLSE) algorithm of AIS (Automatic Identification System) signals decollision in maritime surveillance context. The AIS is a Self-Organized Time Division Multiple Access (SO-TDMA) system, in which vessels periodically transmit information. The main idea of this paper is the decollision of signals received by a Low Earth Orbit (LEO) satellite lead to a global surveillance of maritime traffic using JMLSE algorithm. Simulations are provided in order to evaluate the behavior of the JMLSE algorithm for separation and estimation of sources