Related papers: Uniqueness results on phaseless inverse scattering…
We consider the propagation of acoustic waves at a given wavenumber in a waveguide which is unbounded in one direction. We explain how to construct penetrable obstacles characterized by a physical coefficient $\rho$ which are invisible in…
We prove uniqueness in inverse acoustic scattering in the case the density of the medium has an unbounded gradient across $\Sigma\subseteq\Gamma=\partial\Omega$, where $\Omega$ is a bounded open subset of $\mathbb{R}^{3}$ with a Lipschitz…
For problems of time-harmonic scattering by rational polygonal obstacles, embedding formulae express the far-field pattern induced by any incident plane wave in terms of the far-field patterns for a relatively small (frequency-independent)…
The problem of reconstruction of an unknown refractive index $k(x)$ of an inhomogeneous solid $P$ is considered. The refractive index is assumed to be a piecewise-H\"{o}lder function The original boundary value problem for the Helmholtz…
We determine the uniqueness on starlike obstacles by using the cross section data. We see cross section data as spectral measure in polar coordinate at far field. Cross section scattering data suffice to give the local behavior of the wave…
We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field…
The inverse problem we consider is to reconstruct the location and shape of buried obstacles in the lower half-space of an unbounded two-layered medium in two dimensions from phaseless far-field data. A main difficulty of this problem is…
This paper is concerned with an inverse transmission problem for recovering the shape of a penetrable rectangular grating sitting on a perfectly conducting plate. We consider a general transmission problem with the coefficient \lambda\neq 1…
We propose in this paper a globally numerical method to solve a phaseless coefficient inverse problem: how to reconstruct the spatially distributed refractive index of scatterers from the intensity (modulus square) of the full complex…
This paper develops an efficient numerical method for the inverse scattering problem of a time-harmonic plane wave incident on a perfectly reflecting random periodic structure. The method is based on a novel combination of the Monte Carlo…
We study the fixed angle inverse scattering problem of determining a sound speed from scattering measurements corresponding to a single incident wave. The main result shows that a sound speed close to constant can be stably determined by…
The inverse scattering problem is of critical importance in a number of fields, including medical imaging, sonar, sensing, non-destructive evaluation, and several others. The problem of interest can vary from detecting the shape to the…
In this work, we consider the problem of reconstructing the shape of a three dimensional impenetrable sound-soft axis-symmetric obstacle from measurements of the scattered field at multiple frequencies. This problem has important…
This paper concerns the stability on the inverse source scattering problem for the one-dimensional Helmholtz equation in a two-layered medium. We show that the increasing stability can be achieved by using multi-frequency wave field at the…
In this work, we investigate the shape identification and coefficient determination associated with two time-dependent partial differential equations in two dimensions. We consider the inverse problems of determining a convex polygonal…
In this paper, we prove the local uniqueness of an inverse problem arising in the nonstationary flow of a nonhomogeneous incompressible asymmetric fluid in a bounded domain with smooth boundary. The direct problem is an initial-boundary…
Solving the wave equation is essential to seismic imaging and inversion. The numerical solution of the Helmholtz equation, fundamental to this process, often encounters significant computational and memory challenges. We propose an…
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…
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…
We study the wave equation in a bounded domain or on a compact Riemannian manifold with boundary. Assume that we are given the hyperbolic Neumann-to-Dirichlet map on the boundary corresponding to physical boundary measurements. We consider…