Abstract
This study concerns the problem of the reconstruction of inclusions embedded in a conductive medium in the context of electrical impedance tomography (EIT), which is investigated within the framework of a non-iterative sampling approach. This type of identification strategy relies on the construction of a special indicator function that takes, roughly speaking, small values outside the inclusion and large values inside. Such a function is constructed in this paper from the projection of a fundamental singular solution onto the space spanned by the singular vectors associated with some of the smallest singular values of the data-to-measurement operator. The behavior of the novel indicator function is analyzed. For a subsequent implementation in a discrete setting, the quality of classical finite-dimensional approximations of the measurement operator is discussed. The robustness of this approach is also analyzed when only noisy spectral information is available. Finally, this identification method is implemented numerically and experimentally, and its efficiency is discussed on a set of, partly experimental, examples.
Highlights
Electrical Impedance Tomography (EIT) is an imaging technique for the reconstruction of objects embedded in a given conductive background medium Ω
This study concerns the development of a qualitative approach for the identification of inclusions embedded in a conducting background domain given a set of imposed currents on the domain boundary and the measurement of the corresponding external voltages. This setting provides the access to the relative Neumann-to-Dirichlet operator which, by synthesizing the measurements, encapsulates the available information on the medium internal structure
Rather than exploiting the eigenfunctions associated with the largest eigenvalues of the data-to-measurement operator and which commonly span its signal subspace, the approach developed in this article is based on the extraction of information from its noise subspace
Summary
Electrical Impedance Tomography (EIT) is an imaging technique for the reconstruction of objects embedded in a given conductive background medium Ω. Applications range over a broad spectrum such as non-destructive material testing or tumor detection in medical imaging. This approach aims at determining the internal electrical conductivity map γ of the perturbed domain considered from boundary measurements of a current f and the associated electric potential u. These measurements represent respectively the Neumann and Dirichlet boundary data of the corresponding problem of diffusion.
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