Related papers: Jointly determining the point sources and obstacle…
We investigate the inverse Cauchy and data completion problems for elliptic partial differential equations in a bounded domain $D \subset \mathbb{R}^d$, $d \ge 2$, with a special emphasis on the steady-state heat conduction in anisotropic…
Starting with far field data of time-harmonic acoustic or electromagnetic waves radiated by a collection of compactly supported sources in two-dimensional free space, we develop criteria and algorithms for the recovery of the far field…
A quality-Bayesian approach, combining the direct sampling method and the Bayesian inversion, is proposed to reconstruct the locations and intensities of the unknown acoustic sources using partial data. First, we extend the direct sampling…
In this work, we propose an innovative iterative direct sampling method to solve nonlinear elliptic inverse problems from a limited number of pairs of Cauchy data. It extends the original direct sampling method (DSM) by incorporating an…
We consider the problem of reconstruction of Cauchy data for the wave equation in $\mathbb{R}^1$ by the measurements of its solution on the boundary of the finite interval. This is a one-dimensional model for the multidimensional problem of…
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…
We present a method to compute dispersive shock wave solutions of the Korteweg-de Vries equation that emerge from initial data with step-like boundary conditions at infinity. We derive two different Riemann-Hilbert problems associated with…
The forward problem here is the Cauchy problem for a 1D hyperbolic PDE with a variable coefficient in the principal part of the operator. That coefficient is the spatially distributed dielectric constant. The inverse problem consists of the…
We consider an inverse source problem for the Helmholtz equation in a bounded domain. The problem is to reconstruct the shape of the support of a source term from the Cauchy data on the boundary of the solution of the governing equation. We…
In this paper, we consider the inverse scattering problem associated with an anisotropic medium with a conductive boundary condition. We will assume that the corresponding far--field pattern or Cauchy data is either known or measured. The…
Direct imaging methods recover the presence, position, and shape of the unknown obstacles in time-harmonic inverse scattering without a priori knowledge of either the physical properties or the number of disconnected components of the…
In this work we investigate an inverse coefficient problem for the one-dimensional subdiffusion model, which involves a Caputo fractional derivative in time. The inverse problem is to determine two coefficients and multiple parameters (the…
We study an inverse random obstacle scattering problems in $\mathbb{R}^2$ where the scatterer is formulated by a Gaussian process defined on the angular parameter domain. Equipped with a modified covariance function which is mathematically…
We consider an inverse shape problem for recovering an unknown simply supported obstacle in two dimensions from near--field point--source measurements for the biharmonic Helmholtz equation. The measured data consist of the scattered field…
This short paper is concerned with the numerical reconstruction of small sources from boundary Cauchy data for a single frequency. We study a sampling method to determine the location of small sources in a very fast and robust way.…
We consider the inverse elastic scattering problems using the far field data due to one incident plane wave. A simple method is proposed to reconstruct the location and size of the obstacle using different components of the far field…
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 inverse scattering problems, a model that allows for the simultaneous recovery of both the domain shape and an impedance boundary condition covers a wide range of problems with impenetrable domains, including recovering the shape of…
The problem of mixed signals occurs in many different contexts; one of the most familiar being acoustics. The forward problem in acoustics consists of finding the sound pressure levels at various detectors resulting from sound signals…
This paper is devoted to a novel quantitative imaging scheme of identifying impenetrable obstacles in time-harmonic acoustic scattering from the associated far-field data. The proposed method consists of two phases. In the first phase, we…