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This letter announces and summarizes results obtained in arXiv:1111.5051 and considers several natural extensions. The aforementioned paper proposes a procedure to reconstruct coefficients in a second-order, scalar, elliptic equation from…

Analysis of PDEs · Mathematics 2012-03-07 Guillaume Bal , Gunther Uhlmann

We consider the inverse problem of determining an elastic dislocation that models a seismic fault in the quasi-static regime of aseismic, creeping faults, from displacement measurements made at the surface of Earth. We derive both a…

Analysis of PDEs · Mathematics 2024-10-08 Andrea Aspri , Elena Beretta , Arum Lee , Anna Mazzucato

In this paper we consider inverse problems for resistor networks and for models obtained via the Finite Element Method (FEM) for the conductivity equation. These correspond to discrete versions of the inverse conductivity problem of…

Analysis of PDEs · Mathematics 2013-07-10 Matti Lassas , Mikko Salo , Leo Tzou

We present a general framework to study uniqueness, stability and reconstruction for infinite-dimensional inverse problems when only a finite-dimensional approximation of the measurements is available. For a large class of inverse problems…

Analysis of PDEs · Mathematics 2021-11-10 Giovanni S. Alberti , Matteo Santacesaria

At the High Luminosity Large Hadron Collider (HL-LHC), traditional track reconstruction techniques that are critical for analysis are expected to face challenges due to scaling with track density. Quantum annealing has shown promise in its…

We present a few ways of using conformal maps in the reconstruction of two-dimensional conductivities in electrical impedance tomography. First, by utilizing the Riemann mapping theorem, we can transform any simply connected domain of…

Numerical Analysis · Mathematics 2017-02-27 Nuutti Hyvönen , Lassi Päivärinta , Janne P. Tamminen

Let $X$ be a smooth bordered surface in $\real^3$ with smooth boundary and $\hat \sigma$ a smooth anisotropic conductivity on $X$. If the genus of $X$ is given, then starting from the Dirichlet-to-Neumann operator $\Lambda_{\hat \sigma}$ on…

Mathematical Physics · Physics 2012-04-13 Gennadi Henkin , Matteo Santacesaria

Three-dimensional particle reconstruction with limited two-dimensional projections is an under-determined inverse problem that the exact solution is often difficult to be obtained. In general, approximate solutions can be obtained by…

Image and Video Processing · Electrical Eng. & Systems 2021-09-14 Qi Gao , Shaowu Pan , Hongping Wang , Runjie Wei , Jinjun Wang

This paper is concerned with the inverse problem of reconstructing an inhomogeneous medium from the acoustic far-field data at a fixed frequency in two dimensions. This inverse problem is severely ill-posed (and also strongly nonlinear),…

Numerical Analysis · Mathematics 2023-09-21 Kai Li , Bo Zhang , Haiwen Zhang

Given a space it is easy to obtain the system of geodesic equations on it. In this paper the inverse problem of reconstructing the space from the geodesic equations is addressed. A procedure is developed for obtaining the metric tensor from…

Differential Geometry · Mathematics 2009-11-13 E. Fredericks , F. M. Mahomed , E. Momoniat , Asghar Qadir

This paper concerns the inverse problem of determining a planar conductivity inclusion. Our aim is to analytically recover from the generalized polarization tensors (GPTs), which can be obtained from exterior measurements, a homogeneous…

Analysis of PDEs · Mathematics 2023-01-20 Doosung Choi , Johan Helsing , Sangwoo Kang , Mikyoung Lim

We consider the inverse elastic scattering of incident plane compressional and shear waves from the knowledge of the far field patterns. Specifically, three direct sampling methods for location and shape reconstruction are proposed using…

Numerical Analysis · Mathematics 2018-03-14 Xia Ji , Xiaodong Liu , Yingxia Xi

We consider an electrically conductive compact two-dimensional Riemannian manifold with smooth boundary. This setting defines a natural conductive Laplacian on the manifold and hence also voltage potentials, current fields and corresponding…

Analysis of PDEs · Mathematics 2023-07-04 Kim Knudsen , Steen Markvorsen , Hjørdis Schlüter

We develop a linearized boundary control method for the inverse boundary value problem of determining a density in the acoustic wave equation. The objective is to reconstruct an unknown perturbation in a known background density from the…

Analysis of PDEs · Mathematics 2024-05-27 Lauri Oksanen , Tianyu Yang , Yang Yang

In this paper, we are interested in an inverse problem for the active scalar equations with fractional dissipation on the torus. We perform a second order linearization to relate our model to the linear fractional diffusion equation. Our…

Analysis of PDEs · Mathematics 2025-09-04 Li Li , Weinan Wang

We introduce a method of solving inverse boundary value problems for wave equations on Lorentzian manifolds, and show that zeroth order coefficients can be recovered under certain curvature bounds. The set of Lorentzian metrics satisfying…

Analysis of PDEs · Mathematics 2023-05-10 Spyros Alexakis , Ali Feizmohammadi , Lauri Oksanen

We study an inverse resonance problem on the line in which we aim at determining a compactly supported and integrable perturbation of a fixed P\"oschl-Teller potential. We define the resonances as the poles of the reflection coefficients…

Analysis of PDEs · Mathematics 2026-02-03 Valentin Arrigoni

We consider an inverse initial-data problem for the compressible anisotropic Navier--Stokes equations, in which the goal is to reconstruct the initial velocity field from noisy lateral boundary observations. In the formulation studied here,…

Numerical Analysis · Mathematics 2026-03-06 Cong B. Van , Thuy T. Le , Loc H. Nguyen

Modern reconstruction methods for magnetic resonance imaging (MRI) exploit the spatially varying sensitivity profiles of receive-coil arrays as additional source of information. This allows to reduce the number of time-consuming…

Medical Physics · Physics 2017-09-12 Martin Uecker

A novel and detailed convergence analysis is presented for a greedy algorithm that was previously introduced for operator reconstruction problems in the field of quantum mechanics. This algorithm is based on an offline/online decomposition…

Optimization and Control · Mathematics 2020-11-02 S Buchwald , G Ciaramella , Julien Salomon