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We consider the inverse boundary value problem for the system of equations describing elastic waves in isotropic media on a bounded domain in $\mathbb{R}^3$ via a finite-time Laplace transform. The data is the dynamical Dirichlet-to-Neumann…

Analysis of PDEs · Mathematics 2017-02-10 Maarten V. de Hoop , Gen Nakamura , Jian Zhai

Dix formulated the inverse problem of recovering an elastic body from the measurements of wave fronts of point sources. We geometrize this problem in the context of seismology, leading to the geometrical inverse problem of recovering a…

Differential Geometry · Mathematics 2025-03-14 Maarten V. de Hoop , Joonas Ilmavirta , Matti Lassas

This paper investigates the shape reconstructions of sub-wavelength objects from near-field measurements in transverse electromagnetic scattering. This geometric inverse problem is notoriously ill-posed and challenging. We develop a novel…

Mathematical Physics · Physics 2023-05-03 M. H. Ding , H. Y. Liu , G. H. Zheng

In this article we deal with a class of geometric inverse problem for bottom detection by one single measurement on the free surface in water--waves. We found upper and lower bounds for the size of the region enclosed between two different…

Analysis of PDEs · Mathematics 2020-12-02 R. Lecaros , J. López-Ríos , J. H. Ortega , S. Zamorano

We are concerned with the inverse scattering problem of extracting the geometric structures of an unknown/inaccessible inhomogeneous medium by using the corresponding acoustic far-field measurement. Using the intrinsic geometric properties…

Analysis of PDEs · Mathematics 2017-06-15 Jingzhi Li , Xiaofei Li , Hongyu Liu

Topological concepts open many new horizons for photonic devices, from integrated optics to lasers. The complexity of large scale topological devices asks for an effective solution of the inverse problem: how best to engineer the topology…

Optics · Physics 2018-03-09 Laura Pilozzi , Francis A. Farrelly , Giulia Marcucci , Claudio Conti

In this work we develop and analyze an adaptive finite element method for efficiently solving electrical impedance tomography -- a severely ill-posed nonlinear inverse problem for recovering the conductivity from boundary voltage…

Numerical Analysis · Mathematics 2019-05-16 Bangti Jin , Yifeng Xu , Jun Zou

We consider the imaging problem of the reconstruction of a three-dimensional object via optical diffraction tomography under the assumptions of the Born approximation. Our focus lies in the situation that a rigid object performs an…

Numerical Analysis · Mathematics 2024-07-11 Robert Beinert , Michael Quellmalz

We investigate the inverse source problem for the wave equation, arising in photo- and thermoacoustic tomography. There exist quite a few theoretically exact inversion formulas explicitly expressing solution of this problem in terms of the…

Analysis of PDEs · Mathematics 2018-08-01 Ngoc Do , Leonid Kunyansky

We consider the problem of estimating parameters in large-scale weakly nonlinear inverse problems for which the underlying governing equations is a linear, time-dependent, parabolic partial differential equation. A major challenge in…

Numerical Analysis · Mathematics 2016-05-04 Tania Bakhos , Arvind K. Saibaba , Peter K. Kitanidis

Missing transverse momentum is a crucial observable for physics at hadron colliders, being the only constraint on the kinematics of "invisible" objects such as neutrinos and hypothetical dark matter particles. Computing missing transverse…

Ill-posed linear inverse problems (ILIP), such as restoration and reconstruction, are a core topic of signal/image processing. A standard approach to deal with ILIP uses a constrained optimization problem, where a regularization function is…

Optimization and Control · Mathematics 2016-11-15 Manya V. Afonso , Jose M. Bioucas-Dias , Mario A. T. Figueiredo

In this paper we study an inverse boundary value problem for Maxwell's equations. The goal is to reconstruct perturbations in the refractive index of the medium inside an object from the knowledge of the tangential trace of an electric…

Numerical Analysis · Mathematics 2024-10-04 Jérémy Heleine

We deal with the geometrical inverse problem of the shape reconstruction of cavities in a bounded linear isotropic medium by means of boundary data. The problem is addressed from the point of view of optimal control: the goal is to minimize…

Analysis of PDEs · Mathematics 2022-07-26 Andrea Aspri

We consider the Dirichlet-to-Neumann operator and the direct and inverse Calder\'on's mappings appearing in the Inverse Problem of recovering a smooth bounded and positive isotropic conductivity of a material filling a smooth bounded domain…

Analysis of PDEs · Mathematics 2024-04-16 Javier Castro , Claudio Muñoz , Nicolás Valenzuela

A radial transverse resonance model for two cylindrical concentric layers with different complex dielectric constants is presented. An inverse problem with four unknowns - 3 physical material parameters and one dimensional dielectric layer…

Optics · Physics 2016-03-24 Anders Eriksson , Truls Martin Larsen , Larisa Beilina

In numerical existence proofs for solutions of the semi-linear elliptic system, evaluating the norm of the inverse of a perturbed Laplace operator plays an important role. We reveal an eigenvalue problem to design a method for verifying the…

Numerical Analysis · Mathematics 2021-12-15 Kouta Sekine , Kazuaki Tanaka , Shin'ichi Oishi

In this paper, we develop and numerically implement a novel approach for solving the inverse source problem of the acoustic wave equation in three dimensions. By injecting a small high-contrast droplet into the medium, we exploit the…

Numerical Analysis · Mathematics 2026-01-23 Shutong Hou , Mourad Sini , Haibing Wang

The inverse problem of electrical impedance tomography is severely ill-posed, meaning that, only limited information about the conductivity can in practice be recovered from boundary measurements of electric current and voltage. Recently it…

Analysis of PDEs · Mathematics 2018-09-20 Henrik Garde , Stratos Staboulis

The inverse source problem arising in photoacoustic tomography and in several other coupled-physics modalities is frequently solved by iterative algorithms. Such algorithms are based on the minimization of a certain cost functional. In…

Image and Video Processing · Electrical Eng. & Systems 2025-10-29 Andreas Hauptmann , Leonid Kunyansky , Jenni Poimala