Krylov subspace iterative techniques: on the detection of brain activity with electrical impedance tomography

Polydorides, N. and Lionheart, W.R.B. and McCann, H. (2002) Krylov subspace iterative techniques: on the detection of brain activity with electrical impedance tomography. IEEE Transactions on Medical Imaging, 21 (6). pp. 596-603. ISSN 0278-0062

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Abstract

n this paper, we review some numerical techniques based on the linear Krylov subspace iteration that can be used for the efficient calculation of the forward and the inverse electrical impedance tomography problems. Exploring their computational advantages in solving large-scale systems of equations, we specifically address their implementation in reconstructing localized impedance changes occurring within the human brain. If the conductivity of the head tissues is assumed to be real, the preconditioned conjugate gradients (PCGs) algorithm can be used to calculate efficiently the approximate forward solution to a given error tolerance. The performance and the regularizing properties of the PCG iteration for solving ill-conditioned systems of equations (PCGNs) is then explored, and a suitable preconditioning matrix is suggested in order to enhance its convergence rate. For image reconstruction, the nonlinear inverse problem is considered. Based on the Gauss-Newton method for solving nonlinear problems we have developed two algorithms that implement the PCGN iteration to calculate the linear step solution. Using an anatomically detailed model of the human head and a specific scalp electrode arrangement, images of a simulated impedance change inside brain's white matter have been reconstructed.

Item Type: Article
Additional Information: ©2002 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 53 Differential geometry
MSC 2010, the AMS's Mathematics Subject Classification > 74 Mechanics of deformable solids
MSC 2010, the AMS's Mathematics Subject Classification > 78 Optics, electromagnetic theory
Depositing User: Ms Lucy van Russelt
Date Deposited: 07 Aug 2006
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/444

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