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.In memory of Line Garnero, and of her communicative dedication to unveiling the mysteries of the brain.

International audienceWe present a method to derive a rational model from scattering data for electrical parameter extraction. Unlike other methods, the stability and the MacMillan degree of the rational approximation are guaranteed. In order to improve the usability of our method in computer-aided tuning, we also present an algorithm performing automatic reference plane adjustment. Results obtained on a 10th order dual mode IMUX filter are presented

We are concerned with non-destructive control issues, namely detection and recovery of cracks in a planar (2D) isotropic conductor from partial boundary measurements of a solution to the Laplace–Neumann problem. We first build an extension of that solution to the whole boundary, using constructive approximation techniques in classes of analytic and meromorphic functions, and then use localization algorithms based on boundary computations of the reciprocity gap.

We consider the inverse problem in magnetostatics for recovering the moment of a planar magnetization from measurements of the normal component of the magnetic field at a distance from the support. Such issues arise in studies of magnetic material in general and in paleomagnetism in particular. Assuming the magnetization is a measure with 2 -density, we construct linear forms to be applied on the data in order to estimate the moment. These forms are obtained as solutions to certain extremal problems in Sobolev classes of functions, and their computation reduces to solving an elliptic differential-integral equation, for which synthetic numerical experiments are presented.2010 Mathematics Subject Classification. Primary: 35J15, 35R30, 35A35, 42B37, 86A22; Secondary: 45K05, 46F12, 47N20.* 3 ) −1 , ∇ ⟩ 2 ( ,R 2 ) > 0, ∀ ∈ 1,2 0 ( ), ̸ = 0. Now, the smoothness of the 1,2 0 ( )-valued function ↦ → opt ( ) entails that ↦ → ∇ opt ( ) is continuously differentiable with values in 2 ( , R 2 ), and that

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 in 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 parametrization of the optimization set. This approach guarantees the stability of the MIMO approximant of prescribed McMillan degree.