Related papers: Discretization and Convergence of the EIT Optimal …
This work establishes a general stochastic maximum principle for partially observed optimal control of semi-linear stochastic partial differential equations in a nonconvex control domain. The state evolves in a Hilbert space driven by a…
We consider the inverse multiphase Stefan problem with homogeneous Dirichlet boundary condition on a bounded Lipschitz domain, where the density of the heat source is unknown in addition to the temperature and the phase transition…
This work addresses an optimal control problem for a semilinear elliptic equation in two-dimensional space, characterized by an exponential nonlinearity and a singular source term. The source is modeled as a finite linear combination of…
A path integral Monte Carlo method (PIMC) based on Feynman-Kac formula for mixed boundary conditions of elliptic equations is proposed to solve the forward problem of electrical impedance tomography (EIT) on the boundary to obtain…
An optimal control problem related to the probability of transition between stable states for a thermally driven Ginzburg-Landau equation is considered. The value function for the optimal control problem with a spatial discretization is…
The inverse problem of electrical impedance tomography is severely ill-posed. In particular, the resolution of images produced by impedance tomography deteriorates as the distance from the measurement boundary increases. Such depth…
Optimal control of the singular nonlinear parabolic PDE which is a distributional formulation of multidimensional and multiphase Stefan-type free boundary problem is analyzed. Approximating sequence of finite-dimensional optimal control…
This note is concerned with an optimal control problem governed by the relativistic Maxwell-Newton-Lorentz equations, which describes the motion of charges particles in electro-magnetic fields and consists of a hyperbolic PDE system coupled…
We consider the inverse conductivity problem with discontinuous conductivities. We show in a rigorous way, by a convergence analysis, that one can construct a completely discrete minimization problem whose solution is a good approximation…
This work considers the optimization of electrode positions in head imaging by electrical impedance tomography. The study is motivated by maximizing the sensitivity of electrode measurements to conductivity changes when monitoring the…
This work extends the results of [Garde and Hyv\"onen, Math. Comp. 91:1925-1953] on series reversion for Calder\'on's problem to the case of realistic electrode measurements, with both the internal admittivity of the investigated body and…
In this paper we consider new regularization methods for linear inverse problems of dynamic type. These methods are based on dynamic programming techniques for linear quadratic optimal control problems. Two different approaches are…
In electrical impedance tomography, we aim to solve the conductivity within a target body through electrical measurements made on the surface of the target. This inverse conductivity problem is severely ill-posed, especially in real…
The regularized D-bar method is a popular method for solving Electrical Impedance Tomography (EIT) problems due to its efficiency and simplicity. It utilizes the low-pass truncated scattering data in the non-linear Fourier domain to solve…
We consider an elliptic optimal control problem where the objective functional contains evaluations of the state at a finite number of points. In particular, we use a fidelity term that encourages the state to take certain values at these…
Radon Transformation is generally used to construct optical image (like CT image) from the projection data in biomedical imaging. In this paper, the concept of Radon Transformation is implemented to reconstruct Electrical Impedance…
The first partial boundary data complex geometrical optics based methods for electrical impedance tomography in three dimensions are developed, and tested, on simulated and experimental data. The methods provide good localization of targets…
We propose and analyze a new discretization technique for a linear-quadratic optimal control problem involving the fractional powers of a symmetric and uniformly elliptic second oder operator; control constraints are considered. Since these…
This work is concerned with the optimal control problems governed by a 1D wave equation with variable coefficients and the control spaces $\mathcal M_T$ of either measure-valued functions $L_{w^*}^2(I,\mathcal M(\Omega))$ or vector measures…
In electrical impedance tomography the electrical conductivity inside a physical body is computed from electro-static boundary measurements. The focus of this paper is to extend recent result for the 2D problem to 3D. Prior information…