1,032 research outputs found
The Factorization method for three dimensional Electrical Impedance Tomography
The use of the Factorization method for Electrical Impedance Tomography has
been proved to be very promising for applications in the case where one wants
to find inhomogeneous inclusions in a known background. In many situations, the
inspected domain is three dimensional and is made of various materials. In this
case, the main challenge in applying the Factorization method consists in
computing the Neumann Green's function of the background medium. We explain how
we solve this difficulty and demonstrate the capability of the Factorization
method to locate inclusions in realistic inhomogeneous three dimensional
background media from simulated data obtained by solving the so-called complete
electrode model. We also perform a numerical study of the stability of the
Factorization method with respect to various modelling errors.Comment: 16 page
EIT Reconstruction Algorithms: Pitfalls, Challenges and Recent Developments
We review developments, issues and challenges in Electrical Impedance
Tomography (EIT), for the 4th Workshop on Biomedical Applications of EIT,
Manchester 2003. We focus on the necessity for three dimensional data
collection and reconstruction, efficient solution of the forward problem and
present and future reconstruction algorithms. We also suggest common pitfalls
or ``inverse crimes'' to avoid.Comment: A review paper for the 4th Workshop on Biomedical Applications of
EIT, Manchester, UK, 200
Convergence and regularization for monotonicity-based shape reconstruction in electrical impedance tomography
The inverse problem of electrical impedance tomography is severely ill-posed,
meaning that, only limited information about the conductivity can in practice
be recovered from boundary measurements of electric current and voltage.
Recently it was shown that a simple monotonicity property of the related
Neumann-to-Dirichlet map can be used to characterize shapes of inhomogeneities
in a known background conductivity. In this paper we formulate a
monotonicity-based shape reconstruction scheme that applies to approximative
measurement models, and regularizes against noise and modelling error. We
demonstrate that for admissible choices of regularization parameters the
inhomogeneities are detected, and under reasonable assumptions, asymptotically
exactly characterized. Moreover, we rigorously associate this result with the
complete electrode model, and describe how a computationally cheap
monotonicity-based reconstruction algorithm can be implemented. Numerical
reconstructions from both simulated and real-life measurement data are
presented
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
Parallel algorithms for three dimensional electrical impedance tomography
This thesis is concerned with Electrical Impedance Tomography (EIT), an imaging technique in which pictures of the electrical impedance within a volume are formed from current and voltage measurements made on the surface of the volume. The focus of the thesis is the mathematical and numerical aspects of reconstructing the impedance image from the measured data (the reconstruction problem).
The reconstruction problem is mathematically difficult and most reconstruction algorithms are computationally intensive. Many of the potential applications of EIT in medical diagnosis and industrial process control depend upon rapid reconstruction of images. The aim of this investigation is to find algorithms and numerical techniques that lead to fast reconstruction while respecting the real mathematical difficulties
involved.
A general framework for Newton based reconstruction algorithms is developed which describes a large number of the reconstruction algorithms used by other investigators. Optimal experiments are defined in terms of current drive and voltage measurement patterns and it is shown that adaptive current reconstruction algorithms are a special case of their use. This leads to a new reconstruction algorithm using optimal experiments which is considerably faster than other methods of the Newton type.
A tomograph is tested to measure the magnitude of the major sources of error in the data used for image reconstruction. An investigation into the numerical stability of reconstruction algorithms identifies the resulting uncertainty in the impedance image. A new data collection strategy and a numerical forward model are developed which minimise the effects of, previously, major sources of error.
A reconstruction program is written for a range of Multiple Instruction Multiple Data, (MIMD), distributed memory, parallel computers. These machines promise high computational power for low cost and so look promising as components in medical tomographs. The performance of several reconstruction algorithms on these computers is analysed in detail
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