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We present a non-iterative algorithm to reconstruct the isotropic acoustic wave speed from the measurement of the Neumann-to-Dirichlet map. The algorithm is designed based on the boundary control method and involves only computations that…
We consider boundary measurements for the wave equation on a bounded domain $M \subset \R^2$ or on a compact Riemannian surface, and introduce a method to locate a discontinuity in the wave speed. Assuming that the wave speed consist of an…
We develop a linearized boundary control method for the inverse boundary value problem of determining a potential in the acoustic wave equation from the Neumann-to-Dirichlet map. When the linearization is at the zero potential, we derive a…
In this article we are concerned with an inverse boundary value problem for a non-linear wave equation of divergence form with space dimension $n\geq 3$. In particular the so called the interior determination problem. This non-linear wave…
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…
We study the inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map at selected frequencies as the data. A conditional Lipschitz stability estimate for the inverse problem holds in the case of…
We study the inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map at selected frequency as the data. We develop an explicit reconstruction of the wavespeed using a multi-level nonlinear projected…
We present the results of numerical testing on determination of the sound speed $c$ in the acoustic equation $u_{tt}-c^2\Delta u=0$ by the ${\it boundary}$ ${control}$ ${method}$. The inverse data is a response operator (a hyperbolic…
We consider the following inverse problem: Suppose a $(1+1)$-dimensional wave equation on $\mathbb{R}_+$ with zero initial conditions is excited with a Neumann boundary data modelled as a white noise process. Given also the Dirichlet data…
We develop a linearized boundary control method for the inverse boundary value problem of determining the damping coefficient in the damped wave equation. The objective is to reconstruct an unknown perturbation in a known background damping…
We consider an inverse boundary value problem for a model time-harmonic equation of acoustic tomography of moving fluid with variable current velocity, sound speed, density and absorption. In the present article it is assumed that at fixed…
We develop a linearized boundary control method for the inverse boundary value problem of determining a density in the acoustic wave equation. The objective is to reconstruct an unknown perturbation in a known background density from the…
We consider an inverse problem of recovering a potential associated to a semi-linear wave equation with a quadratic nonlinearity in $1 + 1$ dimensions. We develop a numerical scheme to determine the potential from a noisy…
In this article we deal with a class of geometric inverse problem for bottom detection by one single measurement on the free surface in water--waves. We found upper and lower bounds for the size of the region enclosed between two different…
An inverse boundary value problem for the Helmholtz equation in a bounded domain is considered. The problem is to extract information about an unknown obstacle embedded in the domain with unknown impedance boundary condition (the Robin…
We consider an inverse problem for a hyperbolic partial differential equation on a compact Riemannian manifold. Assuming that $\Gamma_1$ and $\Gamma_2$ are two disjoint open subsets of the boundary of the manifold we define the restricted…
We consider an inverse problem arising in nonlinear ultrasound imaging. The propagation of ultrasound waves is modeled by a quasilinear wave equation. We make measurements at the boundary of the medium encoded in the Dirichlet-to-Neumann…
In this paper, we develop and numerically implement a novel approach for solving the inverse source problem of the acoustic wave equation in three dimensions. By injecting a small high-contrast droplet into the medium, we exploit the…
In this paper, we study the inverse boundary value problem for the wave equation with a view towards an explicit reconstruction procedure. We consider both the anisotropic problem where the unknown is a general Riemannian metric smoothly…
We analyze the inverse problem to reconstruct the shape of a three dimensional homogeneous dielectric obstacle from the knowledge of noisy far field data. The forward problem is solved by a system of second kind boundary integral equations.…