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In this paper, we study the scattering theory for the cubic inhomogeneous Schr\"odinger equations with inverse square potential $iu_t+\Delta u-\frac{a}{|x|^2}u=\lambda |x|^{-b}|u|^2u$ with $a>-\frac14$ and $0<b<1$ in dimension three. In the…

Analysis of PDEs · Mathematics 2021-07-27 Ying Wang

Inverse scattering is the process of estimating the spatial distribution of the scattering potential of an object by measuring the scattered wavefields around it. In this paper, we consider reflection tomography of high contrast objects…

Signal Processing · Electrical Eng. & Systems 2020-12-17 Ajinkya Kadu , Hassan Mansour , Petros T. Boufounos

In the reconstruction process of unknown multiple scattering objects in inverse medium scattering problems, the first important step is to effectively locate some approximate domains that contain all inhomogeneous media. Without such an…

Numerical Analysis · Mathematics 2015-06-12 Keji Liu , Jun Zou

We consider the 3D inverse scattering problem with non-over-determined scattering data. The data are the scattering amplitude $A(\beta, \alpha_0, k)$ for all $\beta \in S_\beta^2$, where $S_\beta^2$ is an open subset of the unit sphere…

Numerical Analysis · Mathematics 2017-02-02 C. Van

Clusters of wave-scattering oscillators offer the ability to passively control wave energy in elastic continua. However, designing such clusters to achieve a desired wave energy pattern is a highly nontrivial task. While the forward…

Signal Processing · Electrical Eng. & Systems 2024-02-29 Joshua R. Tempelman , Tobias Weidemann , Eric B. Flynn , Kathryn H. Matlack , Alexander F. Vakakis

We investigate the regularizing behavior of an iterative Krylov subspace method for the solution of linear inverse problems in precisions lower than double. Recent works have considered the projection of iterated Tikhonov methods using…

Numerical Analysis · Mathematics 2025-12-02 Chelsea Drum , James. G. Nagy , Lucas Onisk

In this paper, a linear model based on multiple measurement vectors model is proposed to formulate the inverse scattering problem of highly conductive objects at one single frequency. Considering the induced currents which are mostly…

Signal Processing · Electrical Eng. & Systems 2019-06-27 Shilong Sun , Bert Jan Kooij , Alexander G. Yarovoy

We present a computational framework for estimating the uncertainty in the numerical solution of linearized infinite-dimensional statistical inverse problems. We adopt the Bayesian inference formulation: given observational data and their…

Numerical Analysis · Mathematics 2013-08-07 Tan Bui-Thanh , Omar Ghattas , James Martin , Georg Stadler

A new numerical method is proposed for a 1-D inverse medium scattering problem with multi-frequency data. This method is based on the construction of a weighted cost functional. The weight is a Carleman Weight Function (CWF). In other…

Numerical Analysis · Mathematics 2017-03-24 Michael V. Klibanov , Aleksandr E. Kolesov , Lam Nguyen , Anders Sullivan

We present a solution method for the inverse scattering problem for integrable two-dimensional relativistic quantum field theories, specified in terms of a given massive single particle spectrum and a factorizing S-matrix. An arbitrary…

Mathematical Physics · Physics 2016-08-09 Sabina Alazzawi , Gandalf Lechner

We present 3D Surface Splatting (3DSS), the first differentiable surface splatting renderer for physically-based inverse rendering from multi-view images. Our central insight is that the surface separation problem at the heart of surface…

Graphics · Computer Science 2026-05-14 Mae Younes , Adnane Boukhayma

We study the numerical solution of forward and inverse acoustic scattering problems by randomly shaped obstacles in three-dimensional space using a fast isogeometric boundary element method. Within the isogeometric framework, realizations…

Numerical Analysis · Mathematics 2020-10-29 Jürgen Dölz , Helmut Harbrecht , Carlos Jerez-Hanckes , Michael Multerer

We analyze the scattering of linear internal waves in a two dimensional channel with subcritical bottom topography. We construct the scattering matrix for the internal wave problem in a channel with straight ends, mapping incoming data to…

Analysis of PDEs · Mathematics 2025-02-21 Zhenhao Li , Jian Wang , Jared Wunsch

Inverse scattering methods capable of compressive imaging are proposed and analyzed. The methods employ randomly and repeatedly (multiple-shot) the single-input-single-output (SISO) measurements in which the probe frequencies, the incident…

Data Analysis, Statistics and Probability · Physics 2015-05-14 Albert C. Fannjiang

Seismic data are commonly modeled by a high-frequency single scattering approximation. This amounts to a linearization in the medium coefficient about a smooth background. The discontinuities are contained in the medium perturbation. The…

Analysis of PDEs · Mathematics 2009-09-25 Christiaan C. Stolk , Maarten V. de Hoop

A special class of integrable nonlinear differential equations related to A.III-type symmetric spaces and having additional reductions are analyzed via the inverse scattering method (ISM). Using the dressing method we construct two classes…

Exactly Solvable and Integrable Systems · Physics 2011-10-21 Vladimir S. Gerdjikov , Georgi G. Grahovski , Alexander V. Mikhailov , Tihomir I. Valchev

This work investigates the scattering coefficients for inverse medium scattering problems. It shows some fundamental properties of the coefficients such as symmetry and tensorial properties. The relationship between the scattering…

Analysis of PDEs · Mathematics 2013-10-24 Habib Ammari , Yat Tin Chow , Jun Zou

Inverse scattering problem is discussed for the Maxwell's equations. A reduction of the Maxwell's system to a new Fredholm second-kind integral equation with a {\it scalar weakly singular kernel} is given for electromagnetic (EM) wave…

Analysis of PDEs · Mathematics 2012-06-27 A. G. Ramm

In this paper we present a hybrid approach to numerically solve two-dimensional electromagnetic inverse scattering problems, whereby the unknown scatterer is hosted by a possibly inhomogeneous background. The approach is `hybrid' in that it…

Analysis of PDEs · Mathematics 2012-10-22 G. Giorgi , M. Brignone , R. Aramini , M. Piana

We present a computational framework for efficient optimization-based "inverse design" of large-area "metasurfaces" (subwavelength-patterned surfaces) for applications such as multi-wavelength and multi-angle optimizations, and…