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We develop a novel wave imaging scheme for reconstructing the shape of an inhomogeneous scatterer and we consider the inverse acoustic obstacle scattering problem as a prototype model for our study. There exists a wealth of reconstruction…

Analysis of PDEs · Mathematics 2020-01-08 Hongyu Liu , Xiaodong Liu , Xianchao Wang , Yuliang Wang

We consider an inverse acoustic scattering problem in simultaneously recovering an embedded obstacle and its surrounding inhomogeneous medium by formally determined far-field data. It is shown that the knowledge of the scattering amplitude…

Analysis of PDEs · Mathematics 2017-05-24 Hongyu Liu , Xiaodong Liu

This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves from a penetrable and buried obstacles. By introducing a related transmission scattering problem, a Newton iteration method is proposed to…

Numerical Analysis · Mathematics 2015-06-12 Haiwen Zhang , Bo Zhang

This paper investigates the inverse biharmonic scattering problems of identifying the shape and location of the obstacle with phased and phaseless measurement data. A direct imaging method based on reverse time migration is proposed for…

Analysis of PDEs · Mathematics 2026-05-12 Tielei Zhu , Zhihao Ge

We consider the inverse elastic scattering problems using the far field data due to one incident plane wave. A simple method is proposed to reconstruct the location and size of the obstacle using different components of the far field…

Analysis of PDEs · Mathematics 2019-04-09 J Liu , X. Liu , J. Sun

In this paper, we consider the inverse problem of determining the location and the shape of a sound-soft obstacle from the modulus of the far-field data for a single incident plane wave. By adding a reference ball artificially to the…

Numerical Analysis · Mathematics 2018-04-17 Heping Dong , Deyue Zhang , Yukun Guo

We consider the inverse acoustic obstacle problem for sound-soft star-shaped obstacles in two dimensions wherein the boundary of the obstacle is determined from measurements of the scattered field at a collection of receivers outside the…

Numerical Analysis · Mathematics 2023-08-04 Mo Zhou , Jiequn Han , Manas Rachh , Carlos Borges

We study an inverse random obstacle scattering problems in $\mathbb{R}^2$ where the scatterer is formulated by a Gaussian process defined on the angular parameter domain. Equipped with a modified covariance function which is mathematically…

Numerical Analysis · Mathematics 2026-02-02 Zhiqi Sun , Xiang Xu , Yiwen Lin

By introducing a shape manifold as a solution set to solve inverse obstacle scattering problems we allow the reconstruction of general, not necessarily star-shaped curves. The bending energy is used as a stabilizing term in Tikhonov…

Numerical Analysis · Mathematics 2020-01-08 Julian Eckhardt , Ralf Hiptmair , Thorsten Hohage , Henrik Schumacher , Max Wardetzky

This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is first established by using…

Analysis of PDEs · Mathematics 2009-12-16 Xiaodong Liu , Bo Zhang

This work is concerned with an inverse elastic scattering problem of identifying the unknown rigid obstacle embedded in an open space filled with a homogeneous and isotropic elastic medium. A Newton-type iteration method relying on the…

Numerical Analysis · Mathematics 2023-10-13 Yan Chang , Yukun Guo , Hongyu Liu , Deyue Zhang

An inverse scattering problem is formulated for reconstructing optical properties of biological tissues. A recursive linearization algorithm is used to solve the inverse scattering problem. We employed the idea of finite element boundary…

Numerical Analysis · Mathematics 2014-04-30 Ying Li

This paper is concerned with the inverse acoustic scattering problem with phaseless total-field data at a fixed frequency. An approximate factorization method is developed to numerically reconstruct both the location and shape of the…

Numerical Analysis · Mathematics 2020-10-15 Bo Zhang , Haiwen Zhang

We propose a novel iterative numerical method to solve the three-dimensional inverse obstacle scattering problem of recovering the shape of the obstacle from far-field measurements. To address the inherent ill-posed nature of the inverse…

Numerical Analysis · Mathematics 2024-04-18 Junqing Chen , Bangti Jin , Haibo Liu

We consider the inverse cracks scattering problems from the far field patterns with a fixed incident direction. We firstly show that the sound-soft cracks can be uniquely determined by the multi-frequency far field patterns with a fixed…

Analysis of PDEs · Mathematics 2024-06-21 Jialei Li , Xiaodong Liu

Inverse scattering problems have many important applications. In this paper, given limited aperture data, we propose a Bayesian method for the inverse acoustic scattering to reconstruct the shape of an obstacle. The inverse problem is…

Analysis of PDEs · Mathematics 2019-05-30 Zhaoxiang Li , Zhiliang Deng , Jiguang Sun

A new sampling method for inverse scattering problems is proposed to process far field data of one incident wave. As the linear sampling method, the method sets up ill-posed integral equations and uses the (approximate) solutions to…

Analysis of PDEs · Mathematics 2018-08-01 Juan Liu , Jiguang Sun

A number of regularization methods for discrete inverse problems consist in considering weighted versions of the usual least square solution. However, these so-called filter methods are generally restricted to monotonic transformations,…

Statistics Theory · Mathematics 2011-05-05 Paul Rochet

This paper is dedicated to design a direct sampling method of inverse electromagnetic scattering problems, which uses multi-frequency sparse backscattering far field data for reconstructing the boundary of perfectly conducting obstacles. We…

Analysis of PDEs · Mathematics 2020-10-28 Tilo Arens , Xia Ji , Xiaodong Liu

We consider an inverse elastic scattering problem of simultaneously reconstructing a rigid obstacle and the excitation sources using near-field measurements. A two-phase numerical method is proposed to achieve the co-inversion of multiple…

Numerical Analysis · Mathematics 2023-07-19 Yan Chang , Yukun Guo , Hongyu Liu , Deyue Zhang