Related papers: Integrating the probe and singular sources methods…
The integrated theory of the probe and singular sources methods (IPS) is developed for an inverse obstacle problem governed by the stationary Schr\"odinger equation in a bounded domain. The unknown obstacles are penetrable, and their…
In this paper, an integrated theory of the probe and singular sources methods for an inverse obstacle problem governed by the Stokes system in a bounded domain is developed. The main results consist of: the probe method for the Stokes…
The Probe Method is an analytical reconstruction scheme for inverse obstacle problems utilizing the Dirichlet-to-Neumann map associated with the governing partial differential equation. It consists of two distinct parts: Side A and Side B.…
The probe and singular sources methods are two well-known classical direct reconstruction methods in inverse obstacle problems governed by partial differential equations. In this paper, by considering an inverse obstacle problem governed by…
This paper gives a note on an application of the enclosure method to an inverse obstacle scattering problem governed by the Helmholtz equation in two dimensions. It is shown that one can uniquely determine the convex hull of an unknown…
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…
This paper is concerned with reconstruction issue of inverse obstacle problems governed by partial differential equations and consists of two parts. (i) The first part considers the foundation of the probe and enclosure methods for an…
A new numerical method to solve an inverse source problem for the Helmholtz equation in inhomogenous media is proposed. This method reduces the original inverse problem to a boundary value problem for a coupled system of elliptic PDEs, in…
This paper is concerned with an inverse wavenumber/frequency-dependent source problem for the Helmholtz equation. In two and three dimensions, the unknown source term is supposed to be compactly supported in spatial variables but…
The problem of recovering acoustic sources, more specifically monopoles, from point-wise measurements of the corresponding acoustic pressure at a limited number of frequencies is addressed. To this purpose, a family of sparse optimization…
The probe method gives a general idea to obtain a reconstruction formula of unknown objects embedded in a known background medium from a mathematical counterpart (the Dirichlet-to-Neumann map) of the measured data of some physical quantity…
A numerical scheme is presented for solving the Helmholtz equation with Dirichlet or Neumann boundary conditions on piecewise smooth open curves, where the curves may have corners and multiple junctions. Existing integral equation methods…
Passive imaging involves recording waves generated by uncontrolled, random sources and utilizing correlations of such waves to image the medium through which they propagate. In this paper, we focus on passive inverse obstacle scattering…
This paper is concerned with reconstruction issue of some typical inverse problems and consists of three parts. First a framework of the enclosure method for an inverse source problem governed by the Helmholtz equation at a fixed wave…
This paper is concerned with an inverse obstacle scattering problem of an acoustic wave for a single incident plane wave and a wave number. The Colton-Sleeman theorem states the unique recovery of sound-soft obstacles with a smooth boundary…
This paper is devoted to the uniqueness in inverse acoustic scattering problems for the Helmholtz equation with phaseless far-field data. Some novel techniques are developed to overcome the difficulty of translation invariance induced by a…
Now a final and maybe simplest formulation of the enclosure method applied to inverse obstacle problems governed by partial differential equations in a {\it spacial domain with an outer boundary} over a finite time interval is fixed. The…
This paper gives a remark on the Enclosure Method by considering inverse obstacle scattering problems with a single incident wave whose governing equation is given by the Helmholtz equation in two dimensions. It is concerned with the…
This paper considers the inverse problem of scattering of time-harmonic acoustic and electromagnetic plane waves by a bounded, inhomogeneous, penetrable obstacle with embedded objects inside. A new method is proposed to prove that the…
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…