Electrical impedance tomography is applied to recover inclusions within a body from electrostatic measurements on the surface of the body. Here, an inclusion is defined to be a region where the electrical conductivity differs significantly from the background. Recently, theoretical foundations have been developed for new techniques to localize inclusions from impedance tomography data. In this paper it is shown that these theoretical results lead quite naturally to noniterative numerical reconstruction algorithms. The algorithms are applied to a number of test cases to compare their performance.
We consider the inverse problem of finding cavities within some body from electrostatic measurements on the boundary. By a cavity we understand any object with a different electrical conductivity than the background material of the body. We survey two algorithms for solving this inverse problem, namely the factorization method and a MUSIC-type algorithm. In particular, we present a number of numerical results to highlight the potential and the limitations of these two methods.We consider an object covering a bounded domain B in R n , n = 2 or 3, with boundary T = ∂ B. It will be assumed that the object is homogeneous and conducting except for a number of insulating cavities j , j = 1, . . . , p (the latter assumption can be relaxed substantially). These are simply connected domains whose closures are mutually disjoint and contained in B. We denote by the union of the cavities and by = ∂ the boundary of . T and are considered to be sufficiently smooth, with ν being the outer (relative to B\ ) unit normal vector.It is well known that, for a prescribed boundary current f ∈ L 2 (T ) = f ∈ L 2 (T ) : T f (s) ds = 0 Recent progress in electrical impedance tomography
Abstract. In this paper we extend recent work on the detection of inclusions using electrostatic measurements to the problem of crack detection in a two-dimensional object. As in the inclusion case our method is based on a factorization of the difference between two Neumann-Dirichlet operators. The factorization possible in the case of cracks is much simpler than that for inclusions and the analysis is greatly simplified. However, the directional information carried by the crack makes the practical implementation of our algorithm more computationally demanding.Mathematics Subject Classification. 35R30, 31A25.
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