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This paper concerns the reconstruction of a scalar coefficient of a second-order elliptic equation in divergence form posed on a bounded domain from internal data. This theory finds applications in multi-wave imaging, greedy methods to…

Analysis of PDEs · Mathematics 2020-05-19 Faouzi Triki , Tao Yin

In coherent diffraction imaging (CDI) experiments, the intensity of the scattered wave impinging on an object is measured on an array of detectors. This signal can be interpreted as the square of the modulus of the Fourier transform of the…

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

Inverse scattering problems are critical in electromagnetic imaging and medical diagnostics but are challenged by their nonlinearity and diverse measurement scenarios. This paper proposes a physics-informed deep contrast source inversion…

Computational Physics · Physics 2025-08-15 Haoran Sun , Daoqi Liu , Hongyu Zhou , Maokun Li , Shenheng Xu , Fan Yang

We investigate the role of retardation corrections to polarizability and to refractive index. We found that the classical electromagnetic theory of dielectrics requires corresponding modifications in terms of nonlocality of the dielectric…

Classical Physics · Physics 2019-05-08 Krzysztof Pachucki , Mariusz Puchalski

A version of the convexification numerical method for a Coefficient Inverse Problem for a 1D hyperbolic PDE is presented. The data for this problem are generated by a single measurement event. This method converges globally. The most…

Numerical Analysis · Mathematics 2020-07-14 Alexey V. Smirnov , Michael V. Klibanov , Loc H. Nguyen

We consider a two-stage numerical procedure for imaging of objects buried in dry sand using time-dependent backscattering experimental radar measurements. These measurements are generated by a single point source of electric pulses and are…

Numerical Analysis · Mathematics 2014-09-04 Larisa Beilina , Nguyen Trung Thành , Michael V. Klibanov , John Bondestam Malmberg

Temporal metamaterials, created by modulating the refractive index in time, offer powerful means of controlling wave propagation but still lack a systematic design methodology. Here, we develop an analytic inverse-design framework rooted in…

We consider a coefficient inverse problem for the dielectric permittivity in Maxwell's equations, with data consisting of boundary measurements of one or two backscattered or transmitted waves. The problem is treated using a Lagrangian…

Numerical Analysis · Mathematics 2016-03-18 John Bondestam Malmberg , Larisa Beilina

We present a novel numerical method to the time-harmonic inverse medium scattering problem of recovering the refractive index from near-field scattered data. The approach consists of two stages, one pruning step of detecting the scatterer…

Numerical Analysis · Mathematics 2015-06-05 Kazufumi Ito , Bangti Jin , Jun Zou

We consider the problem of reconstructing the position and the time-dependent optical properties of a linear dispersive medium from OCT measurements. The medium is multi-layered described by a piece-wise inhomogeneous refractive index. The…

Numerical Analysis · Mathematics 2024-02-23 Peter Elbau , Leonidas Mindrinos , Leopold Veselka

We derive the extension of the classical d'Alembert formula for the wave equation, which provides the analytical solution for the direct scattering problem for a medium with constant refractive index; this is achieved by employing results…

Analysis of PDEs · Mathematics 2025-03-25 Konstantinos Kalimeris , Leonidas Mindrinos

Diffusion models have recently emerged as powerful generative priors for solving inverse problems. However, training diffusion models in the pixel space are both data-intensive and computationally demanding, which restricts their…

Computer Vision and Pattern Recognition · Computer Science 2024-04-17 Bowen Song , Soo Min Kwon , Zecheng Zhang , Xinyu Hu , Qing Qu , Liyue Shen

This paper concerns the reconstruction of a scalar diffusion coefficient $\sigma(x)$ from redundant functionals of the form $H_i(x)=\sigma^{2\alpha}(x)|\nabla u_i|^2(x)$ where $\alpha\in\Rm$ and $u_i$ is a solution of the elliptic problem…

Analysis of PDEs · Mathematics 2012-04-24 Francois Monard , Guillaume Bal

Diffractive lenses have recently been applied to the domain of multispectral imaging in the X-ray and UV regimes where they can achieve very high resolution as compared to reflective and refractive optics. Conventionally, spectral…

Image and Video Processing · Electrical Eng. & Systems 2020-05-26 Evan Widloski , Ulas Kamaci , Farzad Kamalabadi

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

A novel method to solve inverse problems for the wave equation is introduced. The method is a combination of the boundary control method and an iterative time reversal scheme, leading to adaptive imaging of coefficient functions of the wave…

Analysis of PDEs · Mathematics 2007-05-23 Kenrick Bingham , Yaroslav Kurylev , Matti Lassas , Samuli Siltanen

An appealing requirement from the well-known diffraction tomography (DT) exists for success reconstruction from few-view and limited-angle data. Inspired by the well-known compressive sensing (CS), the accurate super-resolution…

Computational Engineering, Finance, and Science · Computer Science 2009-04-20 Lianlin Li , Wenji Zhang , Fang Li

This paper is devoted to the algorithmic development of inverse elastic scattering problems. We focus on reconstructing the locations and shapes of elastic scatterers with known dictionary data for the nearly incompressible materials. The…

Analysis of PDEs · Mathematics 2017-11-02 Li Jingzhi , Liu Hongyu , Sun Hongpeng

We study an inverse scattering problem for a generic hyperbolic system of equations with an unknown coefficient called the reflectivity. The solution of the system models waves (sound, electromagnetic or elastic), and the reflectivity…

Numerical Analysis · Mathematics 2020-02-03 Liliana Borcea , Vladimir Druskin , Alexander V. Mamonov , Mikhail Zaslavsky , Jörn Zimmerling
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