相关论文: Inverse Potential Problems for Divergence of Measu…
We look at continuum solutions in optimisation problems associated to linear inverse problems $y = Ax$ with non-negativity constraint $x \geq 0$. We focus on the case where the noise model leads to maximum likelihood estimation through…
Consider an inverse problem of the simultaneous recovery of boundary impedance and internal conductivity in the electrical impedance tomography (EIT) model using local internal measurement data, which is governed by a boundary value problem…
This work concerns inverse boundary value problems for the time-harmonic Maxwell's equations on differential $1-$forms. We formulate the boundary value problem on a $3-$dimensional compact and simply connected Riemannian manifold $M$ with…
The minimal supersymmetric extension of the standard model allows for some of the coupling strengths to be complex parameters. The presence of such imaginary phases can lead to violations of time reversal invariance, which can be tested if…
The need to blend observational data and mathematical models arises in many applications and leads naturally to inverse problems. Parameters appearing in the model, such as constitutive tensors, initial conditions, boundary conditions, and…
We propose a method to reconstruct the electrical current density from acoustically-modulated boundary measurements of time-harmonic electromagnetic fields. We show that the current can be uniquely reconstructed with Lipschitz stability. We…
The polarization tomography problem consists of recovering a matrix function f from the fundamental matrix of the equation $D\eta/dt=\pi_{\dot\gamma}f\eta$ known for every geodesic $\gamma$ of a given Riemannian metric. Here…
This paper deals with the numerical approximation of the biharmonic inverse source problem in an abstract setting in which the measurement data is finite-dimensional. This unified framework in particular covers the conforming and…
This paper proposes a new mathematical formulation for flow measurement based on the inverse source problem for wave equations with partial boundary measurement. Inspired by the design of acoustic Doppler current profilers (ADCPs), we…
Regularization is a critical technique for ensuring well-posedness in solving inverse problems with incomplete measurement data. Traditionally, the regularization term is designed based on prior knowledge of the unknown signal's…
We study an inverse problem that consists in estimating the first (zero-order) moment of some R2-valued distribution m supported within a closed interval S $\subset$ R, from partial knowledge of the solution to the Poisson-Laplace partial…
We consider inverse problems related to the velocity reconstruction in electrically conducting fluids from externally measured magnetic fields. The underlying theory is presented in the framework of the integral equation approach to…
This paper is concerned with an inverse moving point source problem in electromagnetics. The aim is to reconstruct the moving orbit from the tangential components of magnetic fields taken at a finite number of observation points. The…
In this work, we investigate the regularized solutions and their finite element solutions to the inverse source problems governed by partial differential equations, and establish the stochastic convergence and optimal finite element…
Inverse optimization refers to the inference of unknown parameters of an optimization problem based on knowledge of its optimal solutions. This paper considers inverse optimization in the setting where measurements of the optimal solutions…
In this paper we consider the solution of monotone inverse problems using the particular example of a parameter identification problem for a semilinear parabolic PDE. For the regularized solution of this problem, we introduce a total…
This article studies the inverse problem of recovering a nonlinearity in an elliptic equation $\Delta u + a(x,u) = 0$ from boundary measurements of solutions. Previous results based on first order linearization achieve this under a sign…
Differential regularization is applied to a field theory of a non-relativistic charged boson field $\phi$ with $\lambda (\phi {}^{*} \phi)^2$ self-interaction and coupling to a statistics-changing $U(1)$ Chern-Simons gauge field.…
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…
In this paper, we develop a framework for the discretization of a mixed formulation of quasi-reversibility solutions to ill-posed problems with respect to Poisson's equations. By carefully choosing test and trial spaces a formulation that…