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Reconstructing medical images from partial measurements is an important inverse problem in Computed Tomography (CT) and Magnetic Resonance Imaging (MRI). Existing solutions based on machine learning typically train a model to directly map…

Image and Video Processing · Electrical Eng. & Systems 2022-06-17 Yang Song , Liyue Shen , Lei Xing , Stefano Ermon

This paper is devoted to the investigation of inverse problems related to stationary drift-diffusion equations modeling semiconductor devices. In this context we analyze several identification problems corresponding to different types of…

Analysis of PDEs · Mathematics 2020-11-24 M. Burger , H. W. Engl , A. Leitão , P. A. Markowich

The uniform asymptotic approximation of Green's kernel for the transmission problem of antiplane shear is obtained for domains with small inclusions. The remainder estimates are provided. Numerical simulations are presented to illustrate…

Mathematical Physics · Physics 2010-05-25 Vladimir Maz'ya , Alexander Movchan , Michael Nieves

We present a method to reconstruct the dielectric susceptibility (scattering potential) of an inhomogeneous scattering medium, based on the solution to the inverse scattering problem with internal sources. We employ the theory of…

Numerical Analysis · Mathematics 2024-07-18 Yakun Dong , Kamran Sadiq , Otmar Scherzer , John C. Schotland

We present a conditional diffusion model for electromagnetic inverse design that generates structured media geometries directly from target differential scattering cross-section profiles, bypassing expensive iterative optimization. Our 1D…

Machine Learning · Computer Science 2025-11-10 Mikhail Tsukerman , Konstantin Grotov , Pavel Ginzburg

This paper is concerned with the inverse problem to recover the scalar, complex-valued refractive index of a medium from measurements of scattered time-harmonic electromagnetic waves at a fixed frequency. The main results are two…

Numerical Analysis · Mathematics 2017-02-09 Frederic Weidling , Thorsten Hohage

The motion of a quantum particle constrained to a two-dimensional non-compact Riemannian manifold with non-trivial metric can be described by a flat-space Schroedinger-type equation at the cost of introducing local mass and metric and…

Mesoscale and Nanoscale Physics · Physics 2025-12-19 Benjamin Schwager , Theresa Appel , Jamal Berakdar

In this paper, we investigate the interior transmission eigenvalue problem for an inhomogeneous media with conductive boundary conditions. We prove the discreteness and existence of the transmission eigenvalues. We also investigate the…

Analysis of PDEs · Mathematics 2016-10-31 Oleksandr Bondarenko , Isaac Harris , Andreas Kleefeld

A variety of boundary value problems in linear transport theory are expressed as a diffusion equation of the two-way, or forward-backward, type. In such problems boundary data are specified only on part of the boundary, which introduces…

Mathematical Physics · Physics 2019-02-18 Caleb G. Wagner , Richard Beals

Over the last years, deep learning methods have become an increasingly popular choice to solve tasks from the field of inverse problems. Many of these new data-driven methods have produced impressive results, although most only give point…

Image and Video Processing · Electrical Eng. & Systems 2021-10-28 Alexander Denker , Maximilian Schmidt , Johannes Leuschner , Peter Maass

We consider the classical integral equation reformulation of the radiative transport equation (RTE) in a heterogeneous medium, assuming isotropic scattering. We prove an estimate for the norm of the integral operator in this formulation…

Numerical Analysis · Mathematics 2019-03-21 J. C. H. Blake , I. G. Graham , F. Scheben , A. Spence

The problem of imaging extended targets (sources or scatterers) is formulated in the framework of compressed sensing with emphasis on subwavelength resolution. The proposed formulation of the problems of inverse source/scattering is…

Optics · Physics 2009-09-15 Albert C. Fannjiang

Quantum transport properties are instrumental to understanding quantum coherent transport processes. Potential applications of quantum transport are widespread, in areas ranging from quantum information science to quantum engineering, and…

Quantum Physics · Physics 2016-12-04 L. Jin

This paper is concerned with the classical inverse scattering problem to recover the refractive index of a medium given near or far field measurements of scattered time-harmonic acoustic waves. It contains the first rigorous proof of…

Numerical Analysis · Mathematics 2015-06-19 Thorsten Hohage , Frederic Weidling

We demonstrate that simultaneous reconstruction of scattering and absorption of a mesoscopic system using angularly-resolved measurements of scattered light intensity is possible. Image reconstruction is realized based on the algebraic…

Optics · Physics 2011-01-07 Lucia Florescu , John C. Schotland , Vadim A. Markel

We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral…

Geophysics · Physics 2012-05-29 Nick Polydorides , Alireza Aghasi , Eric L. Miller

We consider the nonlinear problem of determining a connection and a Higgs field from the corresponding parallel transport along geodesics on a Riemannian manifold with boundary, in any dimension. The problem can be reduced to an integral…

Analysis of PDEs · Mathematics 2016-10-18 Hanming Zhou

In this paper, we consider the travel time tomography problem for conformal metrics on a bounded domain, which seeks to determine the conformal factor of the metric from the lengths of geodesics joining boundary points. We establish forward…

Differential Geometry · Mathematics 2024-05-28 Ashwin Tarikere , Hanming Zhou

The convergence of Levenberg-Marquard method is discussed for the inverse problem to reconstruct the storage modulus and loss modulus for the so called scalar model by single interior measurement. The scalar model is the most simplest model…

Numerical Analysis · Mathematics 2017-08-01 Yu Jiang , Gen Nakamura

In this work, a novel approach for the solution of the inverse conductivity problem from one and multiple boundary measurements has been developed on the basis of the implication of the framework of BV - functions. The space of the…

Analysis of PDEs · Mathematics 2020-05-20 Antonios Charalambopoulos , Vanessa Markaki , Drosos Kourounis