274 research outputs found
Lipschitz stability for the electrical impedance tomography problem: the complex case
In this paper we investigate the boundary value problem {div(\gamma\nabla
u)=0 in \Omega, u=f on \partial\Omega where is a complex valued
coefficient, satisfying a strong ellipticity condition. In
Electrical Impedance Tomography, represents the admittance of a
conducting body. An interesting issue is the one of determining
uniquely and in a stable way from the knowledge of the Dirichlet-to-Neumann map
. Under the above general assumptions this problem is an open
issue.
In this paper we prove that, if we assume a priori that is piecewise
constant with a bounded known number of unknown values, then Lipschitz
continuity of from holds
Uniqueness and Lipschitz stability for the identification of Lam\'e parameters from boundary measurements
In this paper we consider the problem of determining an unknown pair
, of piecewise constant Lam\'{e} parameters inside a three
dimensional body from the Dirichlet to Neumann map. We prove uniqueness and
Lipschitz continuous dependence of and from the Dirichlet to
Neumann map
A transmission problem on a polygonal partition: regularity and shape differentiability
We consider a transmission problem on a polygonal partition for the
two-dimensional conductivity equation. For suitable classes of partitions we
establish the exact behaviour of the gradient of solutions in a neighbourhood
of the vertexes of the partition. This allows to prove shape differentiability
of solutions and to establish an explicit formula for the shape derivative
A variational method for quantitative photoacoustic tomography with piecewise constant coefficients
In this article, we consider the inverse problem of determining spatially
heterogeneous absorption and diffusion coefficients from a single measurement
of the absorbed energy (in the steady-state diffusion approximation of light
transfer). This problem, which is central in quantitative photoacoustic
tomography, is in general ill-posed since it admits an infinite number of
solution pairs. We show that when the coefficients are known to be piecewise
constant functions, a unique solution can be obtained. For the numerical
determination of the coefficients, we suggest a variational method based based
on an Ambrosio-Tortorelli-approximation of a Mumford-Shah-like functional,
which we implemented numerically and tested on simulated two-dimensional data
Reconstruction of a piecewise constant conductivity on a polygonal partition via shape optimization in EIT
In this paper, we develop a shape optimization-based algorithm for the
electrical impedance tomography (EIT) problem of determining a piecewise
constant conductivity on a polygonal partition from boundary measurements. The
key tool is to use a distributed shape derivative of a suitable cost functional
with respect to movements of the partition. Numerical simulations showing the
robustness and accuracy of the method are presented for simulated test cases in
two dimensions
Inverse boundary value problem for the Helmholtz equation: quantitative conditional Lipschitz stability estimates
We study the inverse boundary value problem for the Helmholtz equation using
the Dirichlet-to-Neumann map at selected frequencies as the data. A conditional
Lipschitz stability estimate for the inverse problem holds in the case of
wavespeeds that are a linear combination of piecewise constant functions
(following a domain partition) and gives a framework in which the scheme
converges. The stability constant grows exponentially as the number of
subdomains in the domain partition increases. We establish an order optimal
upper bound for the stability constant. We eventually realize computational
experiments to demonstrate the stability constant evolution for three
dimensional wavespeed reconstruction.Comment: 21 pages, 7 figures. arXiv admin note: text overlap with
arXiv:1406.239
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