Related papers: A shape optimization approach for electrical imped…
Many inverse problems have to deal with complex, evolving and often not exactly known geometries, e.g. as domains of forward problems modeled by partial differential equations. This makes it desirable to use methods which are robust with…
Shape optimization methods have been proven useful for identifying interfaces in models governed by partial differential equations. Here we consider a class of shape optimization problems constrained by nonlocal equations which involve…
The inverse problem in Acousto-Electric tomography concerns the reconstruction of the electric conductivity in a domain from knowledge of the power density function in the interior of the body. This interior power density results from…
The objective of this study is to address the difficulty of simplifying the geometric model in which a differential problem is formulated, also called defeaturing, while simultaneously ensuring that the accuracy of the solution is…
We develop the shape derivative analysis of solutions to the problem of scattering of time-harmonic electromagnetic waves by a bounded penetrable obstacle. Since boundary integral equations are a classical tool to solve electromagnetic…
In structural optimization, both parameters and shape are relevant for the model performance. Yet, conventional optimization techniques usually consider either parameters or the shape separately. This work addresses this problem by…
This work establishes a framework for solving inverse boundary problems with the geodesic based quadratic Wasserstein distance ($W_{2}$). A general form of the Fr\'echet gradient is systematically derived by optimal transportation (OT)…
Measurements on a subset of the boundary are common in electrical impedance tomography, especially any electrode model can be interpreted as a partial boundary problem. The information obtained is different to full-boundary measurements as…
For the minimization of a nonlinear cost functional $j$ under convex constraints the relaxed projected gradient process $\varphi_{k+1} = \varphi_{k} + \alpha_k(P_H(\varphi_{k}-\lambda_k \nabla_H j(\varphi_{k}))-\varphi_{k})$ is a well known…
We build a new mathematical model of shape optimization for maximizing ionic concentration governed by the multi-physical coupling steady-state Poisson-Nernst-Planck system. Shape sensitivity analysis is performed to obtain the Eulerian…
This paper proposes the estimation of a mutual shape from a set of different segmentation results using both active contours and information theory. The mutual shape is here defined as a consensus shape estimated from a set of different…
We study the Electrical Impedance Tomography Bayesian inverse problem for recovering the conductivity given noisy measurements of the voltage on some boundary surface electrodes. The uncertain conductivity depends linearly on a countable…
We formulate and investigate a statistical inverse problem of a random tomographic nature, where a probability density function on $\mathbb{R}^3$ is to be recovered from observation of finitely many of its two-dimensional projections in…
Electrical impedance tomography (EIT) is a non-invasive imaging method in which an unknown physical body is probed with electric currents applied on the boundary, and the internal conductivity distribution is recovered from the measured…
We consider stochastic optimization problems with possibly nonsmooth integrands posed in Banach spaces and approximate these stochastic programs via a sample-based approaches. We establish the consistency of approximate Clarke stationary…
A novel and highly efficient computational framework for reconstructing binary-type images suitable for models of various complexity seen in diverse biomedical applications is developed and validated. Efficiency in computational speed and…
In this paper we investigate the problem of identifying conductivity in electrical impedance tomography from one boundary measurement. A variational method with total variation regularization is here proposed to tackle this problem. We…
We consider the linearized electrical impedance tomography problem in two dimensions on the unit disk. By a linearization around constant coefficients and using a trigonometric basis, we calculate the linearized Dirichlet-to-Neumann…
In this work, we propose an innovative iterative direct sampling method to solve nonlinear elliptic inverse problems from a limited number of pairs of Cauchy data. It extends the original direct sampling method (DSM) by incorporating an…
Built upon previous work of the authors in (Deckelnick, Herbert, and Hinze, ESAIM: COCV 28 (2022)), we present a general shape optimisation framework based on the method of mappings in the $W^{1,\infty}$ topology together with a suitable…