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In this paper, we consider the inverse shape problem of recovering small and extended isotropic scatterers with a conductive boundary condition. Here, we assume that the measured far-field data is known at a fixed wave number. We will…

Analysis of PDEs · Mathematics 2023-10-13 Rafael Ceja Ayala , Isaac Harris

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

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

We are concerned with the linearized, isotropic and homogeneous elastic scattering problem by (possibly many) small rigid obstacles of arbitrary Lipschitz regular shapes in 3D. Based on the Foldy-Lax approximation, valid under a sufficient…

Analysis of PDEs · Mathematics 2016-10-20 Fadhel Al-Musallam , Durga Prasad Challa , Mourad Sini

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

Microwave imaging is commonly based on the solution of linearized inverse scattering problems by matched filtering algorithms, i.e., by applying the adjoint of the forward scattering operator to the observation data. A more rigorous…

Image and Video Processing · Electrical Eng. & Systems 2024-12-23 Matthias M. Saurer , Han Na , Marius Brinkmann , Thomas F. Eibert

We are interested in the localization of defects in non-absorbing inhomogeneous media with far-field measurements generated by plane waves. In localization problems, most so-called sampling methods are based on a characterization involving…

Numerical Analysis · Mathematics 2013-04-02 Yann Grisel , Jérémie Fourbil , Vincent Mouysset

Consider a time-harmonic elastic point source incident on a bounded obstacle which is embedded in an open space filled with a homogeneous and isotropic elastic medium. This paper is concerned with the inverse problem of recovering the…

Analysis of PDEs · Mathematics 2025-06-02 Chun Liu , Guanghui Hu , Tao Yin , Bo Zhang

The network localization problem with convex and non-convex distance constraints may be modeled as a nonlinear optimization problem. The existing localization techniques are mainly based on convex optimization. In those techniques, the…

Optimization and Control · Mathematics 2017-11-21 Ananya Saha , Buddhadeb Sau

In this paper, we consider two time-harmonic inverse scattering problems of reconstructing penetrable inhomogeneous obstacles from near field measurements. First we appeal to the Born approximation for reconstructing small isotropic…

Analysis of PDEs · Mathematics 2017-01-18 Isaac Harris , Scott Rome

We develop three inverse elastic scattering schemes for locating multiple small, extended and multiscale rigid bodies, respectively. There are some salient and promising features of the proposed methods. The cores of those schemes are…

Analysis of PDEs · Mathematics 2013-10-15 Guanghui Hu , Jingzhi Li , Hongyu Liu , Hongpeng Sun

Consider the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous medium with complex refractive index. We show that an approximate factorization method can be applied to reconstruct the support of the complex…

Numerical Analysis · Mathematics 2019-03-27 Fenglong Qu , Haiwen Zhang

We consider the reconstruction of the shape and the impedance function of an obstacle from measurements of the scattered field at receivers outside the object. The data is assumed to be generated by plane waves impinging on the obstacle…

Numerical Analysis · Mathematics 2021-04-29 Carlos Borges , Manas Rachh

We study an inverse problem for the wave equation where localized wave sources in random scattering media are to be determined from time resolved measurements of the waves at an array of receivers. The sources are far from the array, so the…

Mathematical Physics · Physics 2016-07-18 Liliana Borcea , Ilker Kocyigit

In this paper, we discuss application of iterative Stochastic Optimization routines to the problem of sparse signal recovery from noisy observation. Using Stochastic Mirror Descent algorithm as a building block, we develop a multistage…

Machine Learning · Statistics 2022-03-31 Anatoli Juditsky , Andrei Kulunchakov , Hlib Tsyntseus

This paper is concerned with the inverse medium problem of determining the location and shape of penetrable scattering objects from measurements of the scattered field. We study a sampling indicator function for recovering the scattering…

Numerical Analysis · Mathematics 2023-03-13 Dinh-Liem Nguyen , Trung Truong

The motivation of this work is an inverse problem for the acoustic wave equation, where an array of sensors probes an unknown medium with pulses and measures the scattered waves. The goal of the inversion is to determine from these…

Numerical Analysis · Mathematics 2018-06-18 Liliana Borcea , Vladimir Druskin , Alexander V. Mamonov , Mikhail Zaslavsky

An optical imager that exploits off-center image rotation to encode both the lateral and depth coordinates of point sources in a single snapshot can perform 3D localization and tracking of space debris. When actively illuminated, unresolved…

Instrumentation and Methods for Astrophysics · Physics 2018-12-24 Chao Wang , Robert Plemmons , Sudhakar Prasad , Raymond Chan , Mila Nikolova

We present a comprehensive study of the resolution and stability properties of sparse promoting optimization theories applied to narrow band array imaging of localized scatterers. We consider homogeneous and heterogeneous media, and…

Numerical Analysis · Mathematics 2016-08-24 Anwei Chai , Miguel Moscoso , George Papanicolaou

We consider the problem of obtaining information about an inaccessible half-space from acoustic measurements made in the accessible half-space. If the measurements are of limited precision, some scatterers will be undetectable because their…

Analysis of PDEs · Mathematics 2007-05-23 Margaret Cheney , David Isaacson , Matti Lassas