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This paper is concerned with the reconstruction of the shape of an acoustic obstacle. Based on the use of the tapered waves with very narrow widths illuminating the obstacle, the boundary of the obstacle is reconstructed by a direct imaging…

Numerical Analysis · Mathematics 2024-10-10 Deyue Zhang , Mengjiao Bai , Yan Chang , Yukun Guo

The monotonicity method for the inverse acoustic scattering problem is to understand the inclusion relation between an unknown object and artificial one by comparing the far field operator with artificial operator. This paper introduces the…

Analysis of PDEs · Mathematics 2021-06-16 Tomohiro Daimon , Takashi Furuya , Ryuji Saiin

This work considers a nonlinear inverse source problem in a coupled diffusion equation from the terminal observation. Theoretically, under some conditions on problem data, we build the uniqueness theorem for this inverse problem and show…

Numerical Analysis · Mathematics 2025-04-29 Chunlong Sun , Wenlong Zhang , Zhidong Zhang

In this paper, we establish two sharp quantitative results for the direct and inverse time-harmonic acoustic wave scattering. The first one is concerned with the recovery of the support of an inhomogeneous medium, independent of its…

Analysis of PDEs · Mathematics 2022-01-07 Emilia L. K. Blåsten , Hongyu Liu

We consider the inverse scattering problem for time-harmonic acoustic waves in a medium with pointwise inhomogeneities. In the Foldy-Lax model, the estimation of the scatterers' locations and intensities from far field measurements can be…

Numerical Analysis · Mathematics 2024-07-25 Giovanni S. Alberti , Romain Petit , Matteo Santacesaria

The unscented Kalman filter is an algorithm capable of handling nonlinear scenarios. Uncertainty in process noise covariance may decrease the filter estimation performance or even lead to its divergence. Therefore, it is important to adjust…

Robotics · Computer Science 2026-03-03 Amit Levy , Itzik Klein

We consider the inverse problem of quantitative reconstruction of properties (e.g., bulk modulus, density) of visco-acoustic materials based on measurements of responding waves after stimulation of the medium. Numerical reconstruction is…

Analysis of PDEs · Mathematics 2022-09-20 Florian Faucher , Otmar Scherzer

We are concerned with the inverse scattering problems associated with incomplete measurement data. It is a challenging topic of increasing importance in many practical applications. Based on a prototypical working model, we propose a…

Analysis of PDEs · Mathematics 2019-12-13 Yu Gao , Kai Zhang

Regularization techniques for the numerical solution of inverse scattering problems in two space dimensions are discussed. Assuming that the boundary of a scatterer is its most prominent feature, we exploit as model the class of…

Functional Analysis · Mathematics 2016-05-05 Gitta Kutyniok , Volker Mehrmann , Philipp Petersen

Three papers describing different methods to solve the inverse scattering problem of the reconstruction of the shape and/or impedance of an obstacle have been chosen for analysis. This literature review consists of an evaluation of these…

Numerical Analysis · Mathematics 2022-11-14 Sarika Karanth , Shobha M. Erappa

In this work the numerical solution of acoustic tomography problem based on the iterative and functional-analytical algorithms is considered. The mathematical properties of these algorithms were previously described in works of R.G.Novikov…

Numerical Analysis · Mathematics 2024-01-26 A. S. Shurup

This paper provides an analysis of the linearized inverse problem in multifrequency electrical impedance tomography. We consider an isotropic conductivity distribution with a finite number of unknown inclusions with different frequency…

Numerical Analysis · Mathematics 2016-10-06 Giovanni S. Alberti , Habib Ammari , Bangti Jin , Jin-Keun Seo , Wenlong Zhang

We consider an inverse problem of recovering a potential associated to a semi-linear wave equation with a quadratic nonlinearity in $1 + 1$ dimensions. We develop a numerical scheme to determine the potential from a noisy…

Analysis of PDEs · Mathematics 2022-03-18 Matti Lassas , Tony Liimatainen , Leyter Potenciano-Machado , Teemu Tyni

This paper is concerned with uniqueness in inverse acoustic scattering with phaseless far-field data at a fixed frequency. In our previous work ({\em SIAM J. Appl. Math. \bf78} (2018), 1737-1753), by utilizing spectral properties of the…

Analysis of PDEs · Mathematics 2018-06-26 Xiaoxu Xu , Bo Zhang , Haiwen Zhang

In this work we consider the inverse elastic scattering problem by an inclusion in two dimensions. The elastic inclusion is placed in an isotropic homogeneous elastic medium. The inverse problem, using the third Betti's formula (direct…

Analysis of PDEs · Mathematics 2018-10-22 Roman Chapko , Drossos Gintides , Leonidas Mindrinos

The inverse quantum scattering problem for the perturbed Bessel equation is considered. A direct and practical method for solving the problem is proposed. It allows one to reduce the inverse problem to a system of linear algebraic…

Mathematical Physics · Physics 2020-12-30 Vladislav V. Kravchenko , Elina L. Shishkina , Sergii M. Torba

In this article, we study the inverse scattering problem for the nonlinear fractional Helmholtz equation with cubic nonlinearity in three dimensions, where we recover a compactly supported potential from scattering amplitude.

Analysis of PDEs · Mathematics 2026-03-30 Saumyajit Das , Susovan Pramanik

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 medium problems involve the reconstruction of a spatially varying unknown medium from available observations by exploring a restricted search space of possible solutions. Standard grid-based representations are very general but all…

Numerical Analysis · Mathematics 2020-06-18 Daniel H. Baffet , Marcus J. Grote , Jet Hoe Tang

The reconstruction of physical properties of a medium from boundary measurements, known as inverse scattering problems, presents significant challenges. The present study aims to validate a newly developed convexification method for a 3D…

Numerical Analysis · Mathematics 2023-06-02 Thuy Le , Vo Anh Khoa , Michael Victor Klibanov , Loc Hoang Nguyen , Grant Bidney , Vasily Astratov