相关论文: An integral equation method for the inverse conduc…

This paper deals with numerical methods for reconstruction of inhomogeneous conductivities. We use the concept of Generalized Polarization Tensors, which were introduced in [3], to do reconstruction. Basic resolution and stability analysis…

Electrical Impedance Tomography gives rise to the severely ill-posed Calder\'on problem of determining the electrical conductivity distribution in a bounded domain from knowledge of the associated Dirichlet-to-Neumann map for the governing…

This paper provides an analysis of the linearized inverse problem in multifrequency electrical impedance tomography. We consider an isotropic conductivity distribution with a finite number of unknown inclusions with different frequency…

This paper proposes a new and efficient numerical algorithm for recovering the damping coefficient from the spectrum of a damped wave operator, which is a classical Borg-Levinson inverse spectral problem. The algorithm is based on inverting…

In this paper the problem of recovering a regularized solution of the Fredholm integral equations of the first kind with Hermitian and square-integrable kernels, and with data corrupted by additive noise, is considered. Instead of using a…

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…

Recursively compressed inverse preconditioning (RCIP) is a kernel-independent and purely numerical method for solving Fredholm second kind boundary integral equations in situations where the boundary shape induces a non-smooth behavior in…

A Coefficient Inverse Problem for the radiative transport equation is considered. The globally convergent numerical method, the so-called convexification, is developed. For the first time, the viscosity solution is considered for a boundary…

Based upon elements of the modern Pseudoanalytic Function Theory, we analyse a new method for numerically approaching the solution of the Dirichlet boundary value problem, corresponding to the two-dimensional Electrical Impedance Equation.…

We consider an inverse problem of reconstructing a degeneracy point in the diffusion coefficient in a one-dimensional parabolic equation by measuring the normal derivative on one side of the domain boundary. We analyze the sensitivity of…

This paper considers the non-linear inverse problem of reconstructing an electric conductivity distribution from the interior power density in a bounded domain. Applications include the novel tomographic method known as acousto-electric…

In this paper, we consider the inverse scattering problem associated with an inhomogeneous media with a conductive boundary. First, we discuss the inverse conductivity problem of reconstructing the conductivity parameter from scattering…

This paper investigates an inverse source problem for space-time fractional diffusion equations from a posteriori interior measurements. The uniqueness result is established by the memory effect of fractional derivatives and the unique…

In this paper we study a linear inverse problem with a biological interpretation, which is modeled by a Fredholm integral equation of the first kind. When the kernel in the Fredholm equation is represented by step func- tions, we obtain…

This paper is concerned with an inverse obstacle problem for the Laplace's equation. The aim is to recover the constant conductivity coefficient in the equation and the boundary of a Dirichlet polygonal obstacle from a single pair of Cauchy…

We propose and test stable algorithms for the reconstruction of the internal conductivity of a biological object using acousto-electric measurements. Namely, the conventional impedance tomography scheme is supplemented by scanning the…

Inverse problems arise in a number of domains such as medical imaging, remote sensing, and many more, relying on the use of advanced signal and image processing approaches -- such as sparsity-driven techniques -- to determine their…

In this paper, a boundary integral method is used to solve an inverse linear heat conduction problem in two-dimensional bounded domain. An inverse problem of measuring the heat flux from partial (on part of the boundary) dynamic boundary…

Physics has played a fundamental role in medicine sciences, specially in imaging diagnostic. Currently, image reconstruction techniques are already taught in Physics courses and there is a growing interest in new potential applications. The…

In this work, we consider an inverse potential problem in the parabolic equation, where the unknown potential is a space-dependent function and the used measurement is the final time data. The unknown potential in this inverse problem is…