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In this work, we consider the time-harmonic inverse elastic source problem of a fixed frequency for the Navier equation in two dimensions. We show that a convex polygon can be uniquely determined by a single far field measurement. Our…
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…
This paper is concerned with the inverse time harmonic elastic scattering of multiple small and well-resolved cavities in two dimensions. We extend the so-called DORT method to the inverse elastic scattering so that selective focusing can…
In the present work, we discuss a unique solvability of an inverse-source problem with integral transmitting condition for time-fractional mixed type equation in a rectangular domain, where the unknown source term depends on space variable…
The recovery of anomalies from backscattering far field data is a long-standing open problem in inverse scattering theory. We make a first step in this direction by establishing the unique identifiability of convex impenetrable obstacles…
In this paper, we consider the inverse scattering problem associated with an anisotropic medium with a conductive boundary. We will assume that the corresponding far-field pattern is known/measured and we consider two inverse problems.…
We consider the inverse problem of determining the density coefficient appearing in the wave equation from separated point source and point receiver data. Under some assumptions on the coefficients, we prove uniqueness results.
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…
In this paper, we give a positive answer to a challenging open problem for recovering unknown obstacle (which is usually referred to as a scatterer) by acoustic wave probe associated to the Helmholtz equation. We show that the acoustic…
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…
It is proved that an inhomogeneous medium whose boundary contains a weakly singular point of arbitrary order scatters every incoming wave. Similarly, a compactly supported source term with weakly singular points on the boundary always…
We study the inverse scattering from a screen with using only one incoming time--harmonic plane wave but with measurements of the scattered wave done at all directions. Especially we focus on the 2D--case i.e. (inverse) scattering from an…
We consider the direct and inverse scattering problem for a penetrable, isotropic obstacle with a second-order Robin boundary condition, which asymptotically models the delamination of the boundary of the scatterer. We develop a direct…
We consider the Bayesian approach to the inverse problem of recovering the shape of an object from measurements of its scattered acoustic field. Working in the time-harmonic setting, we focus on a Helmholtz transmission problem and then…
This paper investigates the inverse scattering problem for the magnetic Schr\"odinger equation. We first establish the well-posedness of the direct problem through a variational approach under physically meaningful assumptions on the…
We consider the problem of fixed frequency acoustic scattering from a sound-soft flat screen. More precisely the obstacle is restricted to a two-dimensional plane and interacting with a arbitrary incident wave, it scatters acoustic waves to…
We study the inverse problem of recovering a spatially dependent variable order in a time-fractional diffusion model from the boundary flux measurement generated by a single boundary excitation. It arises in the identification of…
We formulate the Schiffer's conjecture in spectral geometry in the context of scattering theory. The problem is equivalent to finding a non-trivial solution in an interior transmission problem. We compare the back-scattering data of the…
Inversion of potential field data is a central technique of remote sensing in physics, geophysics, neuroscience and medical imaging. In spite of intense research, uniqueness theorems for potential-field inversion are scarce. Applied studies…
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…