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The concept of scattering coefficients has played a pivotal role in a broad range of inverse scattering and imaging problems in acoustic, and electromagnetic media. In view of their promising applications in inverse problems related to…
This paper investigates the inverse scattering problem of recovering a sound-soft obstacle using passive measurements taken from randomly distributed point sources. The randomness introduced by these sources poses significant challenges,…
In this paper, we propose a new nonuniform mesh method to simulate acoustic scattering problems in two dimensional periodic structures with non-periodic incident fields numerically. As existing methods are difficult to extend to higher…
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…
Here we discuss a regularized version of the factorization method for positive operators acting on a Hilbert Space. The factorization method is a qualitative reconstruction method that has been used to solve many inverse shape problems. In…
This paper considers the inverse problem of scattering of time-harmonic acoustic and electromagnetic plane waves by a bounded, inhomogeneous, penetrable obstacle with embedded objects inside. A new method is proposed to prove that the…
Consider an exterior problem of the three-dimensional elastic wave equation, which models the scattering of a time-harmonic plane wave by a rigid obstacle. The scattering problem is reformulated into a boundary value problem by introducing…
This paper addresses the electromagnetic inverse scattering problem of determining the location and shape of anisotropic objects from near-field data. We investigate both cases involving the Helmholtz equation and Maxwell's equations for…
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…
Three-dimensional (3D) high-resolution imaging is essential in microscopy, yet light scattering poses significant challenges in achieving it. Here, we present an approach to holographic imaging of spatially incoherent objects through…
Passive imaging involves recording waves generated by uncontrolled, random sources and utilizing correlations of such waves to image the medium through which they propagate. In this paper, we focus on passive inverse obstacle scattering…
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…
This paper investigates the inverse scattering problems using sampling methods with near field measurements. The near field measurements appear in two classical inverse scattering problems: the inverse scattering for obstacles and the…
This paper is concerned with the inverse problem of time-harmonic acoustic scattering by an unbounded, locally rough interface which is assumed to be a local perturbation of a plane. The purpose of this paper is to recover the local…
We consider the numerical approximation of the ill-posed data assimilation problem for stationary convection-diffusion equations and extend our previous analysis in [Numer. Math. 144, 451--477, 2020] to the convection-dominated regime.…
This paper is concerned with the inverse scattering problem for the three-dimensional Maxwell's equations in bi-anisotropic periodic structures. The inverse scattering problem aims to determine the shape of bi-anisotropic periodic…
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…
This paper gives a note on an application of the enclosure method to an inverse obstacle scattering problem governed by the Helmholtz equation in two dimensions. It is shown that one can uniquely determine the convex hull of an unknown…
This paper addresses the inverse obstacle scattering problem of simultaneously reconstructing the obstacle geometry and boundary conditions from multi-frequency near-field backscattering data. We first establish rigorous high-frequency…
The paper studies inverse problems of determining unknown coefficients in various semi-linear and quasi-linear wave equations. We introduce a method to solve inverse problems for non-linear equations using interaction of three waves, that…