Related papers: Calder\'on cavities inverse problem as a shape-fro…
We consider inverse problems related to the velocity reconstruction in electrically conducting fluids from externally measured magnetic fields. The underlying theory is presented in the framework of the integral equation approach to…
Calder\'on's inverse conductivity problem has, so far, only been subject to conditional logarithmic stability for infinite-dimensional classes of conductivities and to Lipschitz stability when restricted to finite-dimensional classes.…
For the first time, we develop in this paper the globally convergent convexification numerical method for a Coefficient Inverse Problem for the 3D Helmholtz equation for the case when the backscattering data are generated by a point source…
We consider the inverse conductivity problem with one measurement for the equation $div((\sigma\_1+(\sigma\_2-\sigma\_1)\chi\_D)\nabla{u})=0$ determining the unknown inclusion $D$ included in $\Omega$. We suppose that $\Omega$ is the unit…
We prove the global uniqueness in determination of the conductivity, the permeability and the permittivity of two dimensional Maxwell's equations by partial Dirichlet-to-Neumann map limited to an arbitrary subboundary.
We present a numerical method to determine the complex acoustic impedance at the open surface of an arbitrarily shaped cavity, associated to an impinging planar acoustic wave with a given wavenumber vector and frequency. We have achieved…
This paper concerns the inverse scattering problem to reconstruct a local perturbation in a periodic structure. Unlike the periodic problems, the periodicity for the scattered field no longer holds, thus classical methods, which reduce…
This paper is concerned with the uniqueness of inverse acoustic scattering problem for cavities with the modulus of the near-fields. With the aid of the reference ball technique and the superpositions of two point sources as the incident…
The Bayesian approach to Inverse Problems relies predominantly on Markov Chain Monte Carlo methods for posterior inference. The typical nonlinear concentration of posterior measure observed in many such Inverse Problems presents severe…
We consider the so called Calder\'on problem which corresponds to the determination of a conductivity appearing in an elliptic equation from boundary measurements. Using several known results we propose a simplified and self contained proof…
We prove uniqueness results for a Calderon type inverse problem for the Hodge Laplacian acting on graded forms on certain manifolds in three dimensions. In particular, we show that partial measurements of the relative-to-absolute or…
We consider a region $M$ in $\mathbb{R}^n$ with boundary $\partial M$ and a metric $g$ on $M$ conformal to the Euclidean metric. We analyze the inverse problem, originally formulated by Dix, of reconstructing $g$ from boundary measurements…
A two-step shape reconstruction method for diffuse optical tomography (DOT) is presented which uses adjoint fields and level sets. The propagation of near-infrared photons in tissue is modeled by the time-dependent linear transport…
We consider the restricted Dirichlet-to-Neumann map $\Lambda^{U,V}_{g,A,q}$ for the wave equation with magnetic potential $A$ and scalar potential $q$, on an admissible Lorentzian manifold $(M, g)$ of dimension $n \geq 3$ with boundary.…
This work deals with the problem of determining a non-homogeneous heat conductivity profile in a steady-state heat conduction boundary-value problem with mixed Dirichlet-Neumann boundary conditions over a bounded domain in $\mathbb{R}^n$,…
We consider the shape reconstruction of a conductivity inclusion in two dimensions. We use the concept of Faber polynomials Polarization Tensors (FPTs) introduced in \cite{choi:2018:GME} to derive an exact shape recovery formula for an…
Nonlinear inverse problems often trade inexpensive but fragile first-order updates against curvature-aware methods such as Gauss-Newton and Levenberg-Marquardt, which obtain stronger directions by repeatedly solving Jacobian-based…
This paper addresses an inverse cavity scattering problem associated with the biharmonic wave equation in two dimensions. The objective is to determine the domain or shape of the cavity. The Green's representations are demonstrated for the…
In this article we introduce an approach for studying the geodesic X-ray transform and related geometric inverse problems by using Carleman estimates. The main result states that on compact negatively curved manifolds (resp. nonpositively…
The characterization of a six- (or seven)-dimensional internal manifold with metric as having positive, zero or negative curvature is expected to be an important aspect of warped compactifications in supergravity. In this context, Douglas…