Jean-Paul Marmorat

Source localization using rational approximation on plane sections

In functional neuroimaging, a crucial problem is to localize active sources within the brain non-invasively, from knowledge of electromagnetic measurements outside the head. Identification of point sources from boundary measurements is an ill-posed inverse problem. In the case of electroencephalography (EEG), measurements are only available at electrode positions, the number of sources is not known in advance and the medium within the head is inhomogeneous. This paper presents a new method for EEG source localization, based on rational approximation techniques in the complex plane. The method is used in the context of a nested sphere head model, in combination with a cortical mapping procedure. Results on simulated data prove the applicability of the method in the context of realistic measurement configurations.

Station keeping of geostationary satellites with on-off electric thrusters

The aim of this paper is to consider the modelling and control issues arising in the design of a station keeping system for geostationary satellites based on on-off electric thrusters. In particular, a model for the dynamics of a geostationary satellite affected by perturbations is derived and the electric station keeping problem is then formulated as an optimisation problem with mixed (continuous and discrete) constraints. Simulation results showing the feasibility of the control task on a spacecraft equipped with electric thrusters are also presented and discussed.

Identification of microwave filters by analytic and rational H2 approximation

In this paper, an original approach to frequency identification is explained and demonstrated through an application in the domain of microwave filters. This approach splits into two stages: a stable and causal model of high degree is first computed from the data (completion stage); then, model reduction is performed to get a rational low order model. In the first stage the most is made of the data taking into account the expected behavior of the filter. A reduced order model is then computed by rational H^2 approximation. A new and efficient method has been developed, improved over the years and implemented to solve this problem. It heavily relies on the underlying Hilbert space structure and on a nice parameterization of the optimization set. This approach guarantees the stability of the MIMO approximant of prescribed McMillan degree.

Active Contour Segmentation with a Parametric Shape Prior: Link with the Shape Gradient

Active contours are adapted to image segmentation by energy minimization. The energies often exhibit local minima, requiring regularization. Such an a priori can be expressed as a shape prior and used in two main ways: (1) a shape prior energy is combined with the segmentation energy into a trade-off between prior compliance and accuracy or (2) the segmentation energy is minimized in the space defined by a parametric shape prior. Methods (1) require the tuning of a data-dependent balance parameter and methods (1) and (2) are often dedicated to a specific prior or contour representation, with the prior and segmentation aspects often meshed together, increasing complexity. A general framework for category (2) is proposed: it is independent of the prior and contour representations and it separates the prior and segmentation aspects. It relies on the relationship shown here between the shape gradient, the prior-induced admissible contour transformations, and the segmentation energy minimization.

Modeling Ship Behavior based on Hidden Markov Models

Since 2001, works in the field of security have been considerably growing. All over the word, public places as markets, parkings, hotels, metro and train stations are permanently threatened by terroristic events. For this reason, researches are working every day to meet the need of security. In this article, we have been interested in securing harbors, equipements and people from any threatening event by studying, classifying and recognizing ships behaviors. We propose to use the probabilistic approach Hidden Markov Models (HMM) because of its promising performance in the field of behaviors learning and recognition. The idea is to gather the map of the port as well as ships trajectories in order to construct a set of models of all ships behaviors. Then, this set is exploited to classify every new ship trajectory moving in the harbor. Map of the harbor allowed the initialization of HMM models of ships behaviors, then the well-known Baum-Welch algorithm was chosen to learn models from ships trajectories obtained from port and finally the forward algorithm was used to classify and recognize every new ship behavior.

Static equilibrium of hyperlestic thin shell: symbolic and numerical computation

We here examine the natural shapes of an hyperelastic thin shell called a Carpentiers joint, when the terminal position is known. More specifically we study a rectangular strip that is a flexible thin shell with a constant curvature in its width and a null curvature in its length, at its unconstrained state. We use the theory of large displacement and small strain for hyperelastic material. We first consider an appropriate parameterization of the joint. Then we compute the Green-St Venant strain tensor with a symbolic computation system and we generate the numerical code to compute the elastic energy. In particular, we make strong use of symbolic elements to resolve some problems with zero division. Numerical minimization of this energy is used to find the shape and a couple of simulation are presented.