Related papers: Acousto-electric Inverse Source Problem
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…
We present an image reconstruction algorithm for the Inverse Conductivity Problem based on reformulating the problem in terms of integral equations. We use as data the values of injected electric currents and of the corresponding induced…
This work considers the inverse dynamic source problem arising from the time-domain fluorescence diffuse optical tomography (FDOT). We recover the dynamic distributions of fluorophores in biological tissue by the one single boundary…
We provide a mathematical analysis and a numerical framework for Lorentz force electrical conductivity imaging. Ultrasonic vibration of a tissue in the presence of a static magnetic field induces an electrical current by the Lorentz force.…
The aim of hybrid inverse problems such as Acousto-Electric Tomography or Current Density Imaging is the reconstruction of the electrical conductivity in a domain that can only be accessed from its exterior. In the inversion procedure, the…
We consider an inverse boundary value problem for a model time-harmonic equation of acoustic tomography of moving fluid with variable current velocity, sound speed, density and absorption. In the present article it is assumed that at fixed…
The inverse problem of reconstructing a source term from boundary measurements, for the wave equation, is revisited. We propose a novel approach to recover the unknown source through measuring the wave fields after injecting small…
The goal in acousto-electric tomography (AET) is to reconstruct an image of the unknown electric conductivity in an object from exterior electrostatic currents and voltages that are measured on the boundary of the object while the object is…
This paper focuses on stability estimates of the inverse random source problems for the polyharmonic, electromagnetic, and elastic wave equations. The source is represented as a microlocally isotropic Gaussian random field, which is defined…
In this work we study the inverse boundary value problem of determining the refractive index in the acoustic equation. It is known that this inverse problem is ill-posed. Nonetheless, we show that the ill-posedness decreases when we…
We present calculations that reconstruct electronic current densities in two stacked layers at known depths, using magnetic field data. Solving this inverse problem requires knowledge of the magnetic field in two planes -- one above both…
An inverse problem of the determination of an initial condition in a hyperbolic equation from the lateral Cauchy data is considered. This problem has applications to the thermoacoustic tomography, as well as to linearized coefficient…
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…
We consider an inverse problem of reconstructing two spatially varying coefficients in an acoustic equation of hyperbolic type using interior data of solutions with suitable choices of initial condition. Using a Carleman estimate, we prove…
The problem of reconstructing the spatial support of an extended radiating electric current source density in a lossy dielectric medium from transient boundary measurements of the electric fields is studied. A time reversal algorithm is…
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 present a refined approach to establish a global Lipschitz stability for an inverse source problem concerning the determination of forcing terms in the wave equation with mixed boundary conditions. It consists of boundary…
In this paper, we develop and numerically implement a novel approach for solving the inverse source problem of the acoustic wave equation in three dimensions. By injecting a small high-contrast droplet into the medium, we exploit the…
We consider the electrostatic inverse boundary value problem also known as electrical impedance tomography (EIT) for the case where the conductivity is a piecewise linear function on a domain $\Omega\subset\mathbb{R}^n$ and we show that a…
We consider the inverse problem of recovering an isotropic electrical conductivity from interior knowledge of the magnitude of one current density field generated by applying current on a set of electrodes. The required interior data can be…