Laurent Seppecher

Laurent Seppecher
Ecole Centrale de Lyon | ECL · Département Mathématiques - Informatique - M.I.

About

18
Publications
1,032
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
126
Citations

Publications

Publications (18)
Preprint
Full-text available
This article aims to present a new method to reconstruct slowly varying width defects in 2D waveguides using locally resonant frequencies. At these frequencies, locally resonant modes propagate in the waveguide under the form of Airy functions depending on a parameter called the locally resonant point. In this particular point, the local width of t...
Preprint
Full-text available
This article aims to present a general study of the Helmholtz problem in slowly varying waveguides. This work is of particular interest at locally resonant frequencies, where a phenomenon close to the tunnel effect for Schr\"odinger equation in quantum mechanics can be observed. In this situation, locally resonant modes propagate in the waveguide u...
Preprint
Full-text available
Localization and reconstruction of small defects in acoustic or electromagnetic waveguides is of crucial interest in nondestructive evaluation of structures. The aim of this work is to present a new multi-frequency inversion method to reconstruct small defects in a 2D waveguide. Given one-side multi-frequency wave field measurements of propagating...
Conference Paper
This study focuses on the reconstruction of the shear modulus contrast in linear elastic and isotropic media, in quasi-static ultrasound elastography. The method proposed is based on the variational formulation of the equilibrium equations and on the choice of adapted discretization spaces to estimate the parameters of interest. Experimental result...
Article
Full-text available
The aim of this paper is to present and analyze a new direct method for solving the linear elasticity inverse problem. Given measurements of some displacement fields inside a medium, we show that a stable reconstruction of elastic parameters is possible, even for discontinuous parameters and without boundary information. We provide a general approa...
Article
Full-text available
Localization and reconstruction of small defects in acoustic or electromagnetic waveguides is of crucial interest in nondestructive evaluation of structures. The aim of this work is to present a new multi-frequency inversion method to reconstruct small defects in a 2D waveguide. Given one-side multi-frequency wave field measurements of propagating...
Article
Full-text available
At the present time, numerical dosimetry has reached a certain level of maturity and dedicated commercial software packages are already available. However, the fast and accurate characterization of exposure in real conditions is still challenging for many reasons. For instance, when the exact body posture has to be considered, the classical approac...
Preprint
Full-text available
The aim of this paper is to present and analyze a new direct method for solving the linear elasticity inverse problem. Given measurements of some displacement fields inside a medium, we show that a stable reconstruction of elastic parameters is possible, even for discontinuous parameters and without boundary information. We provide a general approa...
Article
Full-text available
The aim of this paper is to develop an efficient reconstruction algorithm for ultrasound-modulated diffuse optical tomography. In diffuse op-tical imaging, the resolution is in general low. By mechanically perturbing the medium, we show that it is possible to achieve a significant resolution en-hancement. When a spherical acoustic wave is propagati...
Article
Full-text available
This thesis aims at developing an original mathematical approach for modeling hybrid biomedical imaging modalities. The core idea is to run an ill-posed imaging method while perturbing the medium using mechanical displacements. These displacements described by an elastic wave equation perturb the collected measurements. Using these perturbed measur...
Article
Full-text available
We provide a mathematical analysis of and a numerical framework for full-field optical coherence elastography, which has unique features including micron-scale resolution, real-time processing, and non-invasive imaging. We develop a novel algorithm for transforming volumetric optical images before and after the mechanical solicitation of a sample w...
Article
The aim of this paper is to propose for the first time a reconstruction scheme and a stability result for recovering from acoustic-optic data absorption distributions with bounded variation. The paper extends earlier results in [3] and [5] on smooth absorption distributions. It opens a door for a mathematical and numerical framework for imaging, fr...
Article
We provide a mathematical analysis and a numerical framework for Lorentz force electrical conductivity imaging. Ultrasonic vibration of a tissue in the presence of a static magnetic field induces an electrical current by the Lorentz force. This current can be detected by electrodes placed around the tissue; it is proportional to the velocity of the...
Article
Full-text available
The aim of this paper is to tackle the nonlinear optical reconstruction problem. Given a set of acousto-optic measurements, we develop a mathematical framework for the reconstruction problem in the case where the optical absorption distribution is supposed to be a perturbation of a piecewise constant function. Analyzing the acousto-optic measuremen...
Article
Full-text available
The aim of this paper is to develop a mathematical framework for opto-elastography. In opto-elastography, a mechanical perturbation of the medium produces a decorrelation of optical speckle patterns due to the displacements of optical scatterers. To model this, we consider two optically random media, with the second medium obtained by shifting the...
Article
The aim of this paper is to develop a mathematical framework for acousto-electromagnetic tomography and to introduce an efficient reconstruction algorithm. In electromagnetic wave imaging, the resolution is limited by the Rayleigh criterion, that is, half the operating wavelength. By mechanically perturbing the medium, we show that it is possible t...

Network

Cited By