相关论文: A direct D-bar reconstruction algorithm for recove…

A method for including a priori information in the 2-D D-bar algorithm is presented. Two methods of assigning conductivity values to the prior are presented, each corresponding to a different scenario on applications. The method is tested…

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…

This report extends our recent progress in tackling a challenging 3D inverse scattering problem governed by the Helmholtz equation. Our target application is to reconstruct dielectric constants, electric conductivities and shapes of front…

This paper considers the reconstruction problem in Acousto-Electrical Tomography, i.e., the problem of estimating a spatially varying conductivity in a bounded domain from measurements of the internal power densities resulting from…

We introduce a new integral representation formula in the d-bar Neumann Theory on weakly pseudoconvex domains which satisfies certain estimates analogous to the basic L^2 estimate. It is expected that more complete estimates can be obtained…

In this paper, we deal with the inverse problem of the shape reconstruction of inclusions in elastic bodies. The main idea of this reconstruction is based on the monotonicity property of the Neumann-to-Dirichlet operator presented in a…

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 propose a new approach to implement the density matrix renormalization group (DMRG) in two dimensions. With this approach the initial blocks of a L by L lattice are built up directly from the matrix elements of a (L-1) by L-1) lattice…

Detecting inhomogeneities in the electrical conductivity is a special case of the inverse problem in electrical impedance tomography, that leads to fast direct reconstruction methods. One such method can, under reasonable assumptions,…

Two reconstruction methods of Electrical Impedance Tomography (EIT) are numerically compared for nonsmooth conductivities in the plane based on the use of complex geometrical optics (CGO) solutions to D-bar equations involving the global…

There are a number of clinically relevant tasks in digital breast tomosynthesis (DBT) involving the detection and visual assessment of fiber-like structures such as Cooper's ligaments, blood vessels, and spiculated lesions. Such structures…

Suppose a graph $G$ is stochastically created by uniformly sampling vertices along a line segment and connecting each pair of vertices with a probability that is a known decreasing function of their distance. We ask if it is possible to…

The classical $\overline \partial$-method has been generalized recently [lnv], [lnv2] to be used in the presence of exceptional points. We apply this generalization to solve Dirac inverse scattering problem with weak assumptions on…

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…

This paper develops a new Hilbert space method to characterize a family of reproducing kernel Hilbert spaces of real harmonic functions in a bounded Lipschitz domain $\Omega \subset \mathbb R^d, d\geq 2$ involving some families of positive…

We present a new method for recovering the cosmological density, velocity, and potential fields from all-sky redshift catalogues. The method is based on an expansion of the fields in orthogonal radial (Bessel) and angular (spherical…

We consider the numerical reconstruction of the spatially dependent conductivity coefficient and the source term in elliptic partial differential equations in a two-dimensional convex polygonal domain, with the homogeneous Dirichlet…

We consider an inverse problem of reconstructing the conductivity function in a hyperbolic equation using single space-time domain noisy observations of the solution on the backscattering boundary of the computational domain. We formulate…

We present a reconstruction algorithm for recovering both "magnetic-hard" and "magnetic-soft" obstacles in a background domain with known isotropic medium from the boundary impedance map. We use in our algorithm complex geometric optics…

In this paper, we consider inverse shape problems coming from diffuse optical tomography and inverse scattering. In both problems, our goal is to reconstruct small volume interior regions from measured data on the exterior surface of an…