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Topological Approach to Image Reconstruction in Electrical Impedance Tomography

Authors:
Tomasz Rymarczyk
Paweł Tchórzewski
Jan Sikora

Keywords: Image Reconstruction; Inverse Problem; Level Set Method; Optimization Methods

Abstract:
In this paper, we investigate the application of the topological derivative in combination with the level set method for the topology optimization. The level set method and the gradient technique are based on shape and topology optimization approach to the Electrical Impedance Tomography problems with piecewise constant conductivities. The Finite Element Method and the Boundary Element Method have been used to solve the forward problem. The cost of our numerical algorithm is moderate since the shape is captured on a fixed mesh. The proposed solution algorithm is initialized by using topological sensitivity analysis. Shape derivatives and topological derivatives have been incorporated with the level set method to investigate shape optimization problems. Then it relies on the notion of shape derivatives to update the shape of the domains where conductivity takes different values. The shape derivative measures the sensitivity of boundary perturbations while the topological derivative measures the sensitivity of creating a small object in the interior domain. The coupled algorithm is a relatively new procedure to overcome this problem.

Pages: 42 to 45

Copyright: Copyright (c) IARIA, 2014

Publication date: August 24, 2014

Published in: conference

ISSN: 2308-4499

ISBN: 978-1-61208-354-4

Location: Rome, Italy

Dates: from August 24, 2014 to August 28, 2014