相关论文: Adaptive Reconstruction for Electrical Impedance T…
An adaptive regularization strategy for stabilizing Newton-like iterations on a coarse mesh is developed in the context of adaptive finite element methods for nonlinear PDE. Existence, uniqueness and approximation properties are known for…
We consider Inverse Electrical Impedance Tomography (EIT) problem on recovering electrical conductivity and potential in the body based on the measurement of the boundary voltages on the $m$ electrodes for a given electrode current. The…
The multifrequency electrical impedance tomography is considered in order to image a conductivity inclusion inside a homogeneous background medium by injecting one current. An original spectral decomposition of the solution of the forward…
A new non-linear optimization approach is proposed for the sparse reconstruction of log-conductivities in current density impedance imaging. This framework comprises of minimizing an objective functional involving a least squares fit of the…
In this paper we provide a convergence analysis of some variational methods alternative to the classical Tikhonov regularization, namely Ivanov regularization (also called method of quasi solutions) with some versions of the discrepancy…
Magnetic resonance electrical impedance tomography (MREIT) aims to recover the electrical conductivity distribution of an object using partial information of magnetic flux densities inside the tissue which can be measured using an MRI…
We propose a new method of adaptive piecewise approximation based on Sinc points for ordinary differential equations. The adaptive method is a piecewise collocation method which utilizes Poly-Sinc interpolation to reach a preset level of…
We analyze an adaptive boundary element method for the weakly-singular and hypersingular integral equations for the 2D and 3D Helmholtz problem. The proposed adaptive algorithm is steered by a residual error estimator and does not rely on…
A key observation underlying this paper is the fact that the range invariance condition for convergence of regularization methods for nonlinear ill-posed operator equations -- such as coefficient identification in partial differential…
In this work, we propose and analyse a weak Galerkin method for the electrical impedance tomography based on a bounded variation regularization. We use the complete electrode model as the forward system that is approximated by a weak…
We consider an adaptive algorithm for finite element methods for the isogeometric analysis (IGAFEM) of elliptic (possibly non-symmetric) second-order partial differential equations. We employ analysis-suitable T-splines of arbitrary odd…
We consider the problem of recovering the topology and the edge conductance value, as well as characterizing a set of electrical networks that satisfy the limitedly available Thevenin impedance measurements. The measurements are obtained…
In this paper, we consider the integrating factor midpoint method for wave-type equations and derive optimal order a posteriori error estimates. We first introduce an integrating factor midpoint approximation defined by the piecewise linear…
A new domain decomposition method for Maxwell's equations in conductive media is presented. Using this method reconstruction algorithms are developed for determination of dielectric permittivity function using time-dependent scattered data…
This work introduces a computational framework for applying absolute electrical impedance tomography to head imaging without accurate information on the head shape or the electrode positions. A library of fifty heads is employed to build a…
We present a new approach to convexification of the Tikhonov regularization using a continuation method strategy. We embed the original minimization problem into a one-parameter family of minimization problems. Both the penalty term and the…
This paper is devoted to the analysis of a second order method for recovering the \emph{a priori} unknown shape of an inclusion $\omega$ inside a body $\Omega$ from boundary measurement. This inverse problem - known as electrical impedance…
We develop a novel iterative direct sampling method (IDSM) for solving linear or nonlinear elliptic inverse problems with partial Cauchy data. It integrates three innovations: a data completion scheme to reconstruct missing boundary…
For the linearized reconstruction problem in Electrical Impedance Tomography (EIT) with the Complete Electrode Model (CEM), Lechleiter and Rieder (2008 Inverse Problems 24 065009) have shown that a piecewise polynomial conductivity on a…
This paper is devoted to proving convergence rates of variational and iterative regularization methods under variational source conditions VSCs for inverse problems whose linearization satisfies a range invariance condition. In order to…