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Reconstruction of Space Distribution of Characteristics in Compound Structures by General Ray Method
Published online by Cambridge University Press: 24 February 2014
Abstract
Recognition of material structures, particularly, identification of electrical properties of materials by Electrical Tomography is very important in different applied problems. In a plane case Electrical Tomography can be mathematically described as a coefficient inverse problem for the Laplace type equation, written in the divergent form. The General Ray (GR) Principle, proposed by the author, reduces the Laplace type equation to the family of ordinary differential equations with respect the traces of the potential function and the permittivity function on the lines, which intersect the plane domain. General Ray Principle was realized as General Ray method and fast algorithm for the plane domains. In presented investigation we apply the plane scheme of GR-method for some space domains to identify distribution of structure characteristics inside it. For this we consider the space domain as assemblage of plane slices. Reconstructing desired distribution in each plane slice we obtain then the space internal distribution of electrical characteristics by 3D spline approximation. We consider here specific variant of the measurement scheme for the 3D Electrical Tomography (ET), based on the variant, proposed by the author for the plane domain. Proposed approach gives, in principle, the possibility to use a large number of electrodes, obtain more values of the input data and reconstruct the desired space structure more perfectly. Computer simulation of this 3D scheme is realized as MATLAB software and justified by numerical experiments on simulated examples.
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