Level set reconstruction of conductivity and permittivity from boundary electrical measurements using experimental data

Dorn, O and Lionheart, WRB and Soleimani, M (2006) Level set reconstruction of conductivity and permittivity from boundary electrical measurements using experimental data. Inverse Problems in Science and Engineering, 14 (2). pp. 193-210. ISSN 1741-5977

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A shape reconstruction method for electrical resistance and capacitance tomography is presented using a level set formulation. In this shape reconstruction approach, the conductivity (or permittivity) values of the inhomogeneous background and the obstacles are assumed to be (approximately) known, but the number, sizes, shapes, and locations of these obstacles have to be recovered from the data. A key point in this shape identification technique is to represent geometrical boundaries of the obstacles by using a level set function. This representation of the shapes has the advantage that the level set function automatically handles the splitting or merging of the objects during the reconstruction. Another key point of the algorithm is to solve the inverse problem of finding the interfaces between two materials using a narrow-band method, which not only decreases the number of unknowns and therefore the computational cost of the inversion, but also tends to improve the condition number of the discrete inverse problem compared to pixel (voxel)-based image reconstruction. Level set shape reconstruction results shown in this article are some of the first ones using experimental electrical tomography data. The experimental results also show some improvements in image quality compared with the pixel-based image reconstruction. The proposed technique is applied to 2D resistance and capacitance tomography for both simulated and experimental data. In addition, a full 3D inversion is performed on simulated 3D resistance tomography data.

Item Type: Article
Uncontrolled Keywords: Shape reconstruction, ERT, ECT, Level set function
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 35 Partial differential equations
MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
PACS 2010, the AIP's Physics and Astronomy Classification Scheme > 40 ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID MECHANICS > 41 Electromagnetism; electron and ion optics
Depositing User: Prof WRB Lionheart
Date Deposited: 06 Sep 2006
Last Modified: 20 Oct 2017 14:12
URI: https://eprints.maths.manchester.ac.uk/id/eprint/586

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