LEBLOND , Juliette

We study an inverse problem that consists in estimating the first (zero-order) moment of some R2-valued distribution m supported within a closed interval S ⊂ R, from partial knowledge of the solution to the Poisson-Laplace partial differential equation with source term equal to the divergence of m on another interval parallel to and located at...

In this work, we study some aspects of the solvability of the minimization of a non-convex least-squares criterion involved in dipolar source recovery issues, using boundary values of a solution to a Poisson problem in a domain of dimension 3. This Poisson problem arises in particular from the quasi-static approximation of Maxwell equations...

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We analyze Bergman spaces A p f (D) of generalized analytic functions of solutions to the Vekua equation ∂w = (∂f /f)w in the unit disc of the complex plane, for Lipschitz-smooth non-vanishing real valued functions f and 1 < p < ∞. We consider a family of bounded extremal problems (best constrained approximation) in the Bergman space A p (D)...

This work gives an overview of the solution to linear forward and inverse problems for a class of elliptic partial differential equations in two-dimensional domains Ω, in the framework of Banach spaces and operators. We focus on the equation ∇(σ∇u) = 0, with σ in Sobolev spaces W 1,p (Ω), 1 < p < ∞, with Dirichlet or Neumann or mixed boundary...

The aim of this report is to exhibit a class of stabilizing feedback laws for a structurally undamped one-link flexible arm with control applied at one extremity. A finite-dimensional model of the arm, corresponding to a discretization in space, is first considered. The arm is then modeled by a classical partial differential equation, no finite...

We consider the inverse problem of recovering the position and moment of a magnetic dipolefrom sparse measurements of the field it generates, known on sections of three orthogonal cylindersenclosing it. This problem is motivated by recent measurements performed on Moon rocks, in viewof determining their magnetic properties. The key ingredient...

We consider dipole recovery issues from sparse magnetic data, with the use of best quadratic rational approximation techniques, together with geometrical and algebraic properties of the poles of the approximants.

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We consider the extremal problem of best approximation to some function $f$ in $L^2(I)$, with $I$ a subset of the circle, by the trace of a Hardy function whose modulus is bounded pointwise by some gauge function on the complementary subset.

A fundamental problem in theoretical neurosciences is the inverse problem of source localization, which aims at locating the sources of the electric activity of the functioning human brain using measurements usually acquired by non-invasive imaging techniques, such as the electroencephalography (EEG). EEG measures the effect of the electric...

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In the present article, we study the discrete spectrum of certain bounded Toeplitz operators with harmonic symbol on a Bergman space. Using the methods of classical perturbaton theory and recent results by Borichev-Golinskii-Kupin and Favorov-Golinskii, we obtain a quantitative result on the distribution of the discrete spectrum of the operator...

We consider the Cauchy problem of recovering both Neumann and Dirichlet data on the inner part of the boundary of an annular domain, from measurements of a harmonic function on some part of the outer boundary. The ultimate goal is to compute the impedance or Robin coefficient, which is the quotient of these extended data, on the inner boundary....

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Being given pointwise measurements of the electric potential taken by electrodes on part of the scalp, the EEG (electroencephalography) inverse problem consists in estimating current sources within the brain that account for this activity. A model for the behaviour of the potential rests on Maxwell equation in the quasi-static case, under the...

Electroencephalography (EEG) is a non invasive imaging technique that measures the effect of the electric activity of active brain regions, called sources, through values of the electric potential furnished by a set of electrodes placed at the surface of the scalp. A fundamental problem there is the inverse problem of source localization which...

Electroencephalography (EEG) is a non invasive imaging technique that measures the effect of the electric activity of active brain regions, called sources, through values of the electric potential furnished by a set of electrodes placed at the surface of the scalp. A fundamental problem there is the inverse problem of source localization which...

We discuss recent results on sparse recovery for inverse potential problem with source term in divergence form. The notion of sparsity which is set forth is measure-theoretic, namely pure 1-unrectifiability of the support. The theory applies when a superset of the support is known to be slender, meaning it has measure zero and all connected...