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

Polydorides, Nick; Lionheart, William R B; McCann, H.

doi:10.1109/tmi.2002.800607

Cited by 54 publications

(40 citation statements)

References 21 publications

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“…Relatives of CG for non-symmetric matrices include Generalised Minimal Residual (GMRES) [128], Bi-Conjugate Gradient BiCG, Quasi Minimal Residual (QMR) and Bi-Conjugate Gradient Stabilized (Bi-CGSTAB). All have their own merits [18] and as implementations are readily available have been tried to some extent in EIT forward or inverse solutions, not much [97,68] is published but applications of CG itself to EIT include [121,124,108,116] and to optical tomography [6,7]. The application of Krylov subspace methods to solving elliptic PDEs as well as linear inverse problems [70,32] are active areas of research and we invite the reader to seek out and use the latest developments.…”

Section: Conjugate Gradient and Krylov Subspace Methodsmentioning

confidence: 99%

The reconstruction problem

Lionheart¹,

Polydorides²,

Borsic³

2004

Series in Medical Physics and Biomedical Engineering

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Section: Conjugate Gradient and Krylov Subspace Methodsmentioning

confidence: 99%

The reconstruction problem

Lionheart¹,

Polydorides²,

Borsic³

2004

Series in Medical Physics and Biomedical Engineering

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“…A proposition of such implementation has been presented in Horesh [35] and Polydorides [36]. Notice that the algorithm in Eq.…”

Section: Simulation Setup and Test Proceduresmentioning

confidence: 99%

Absolute Imaging of Low Conductivity Material Distributions Using Nonlinear Reconstruction Methods in Magnetic Induction Tomography

Dekdouk¹,

Ktistis²,

Armitage³

et al. 2016

PIER

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Abstract-Magnetic Induction Tomography (MIT) is a newly developing technique of electrical tomography that in principle is able to map the electrical conductivity distribution in the volume of objects. The image reconstruction problem in MIT is similar to electrical impedance tomography (EIT) in the sense that both seek to recover the conductivity map, but differ remarkably in the fact that data being inverted in MIT is derived from induction theory and related sources of noise are different. Progress in MIT image reconstruction is still limited, and so far mainly linear algorithms have been implemented. In difference imaging, step inversion was demonstrated for recovering perturbations within conductive media, but at the cost of producing qualitative images, whilst in absolute imaging, linear iterative algorithms have mostly been employed but mainly offering encouraging results for imaging isolated high conductive targets.In this paper, we investigate the possibility of absolute imaging in 3D MIT of a target within conductive medium for low conductivity application (σ < 5 Sm −1 ). For this class of problems, the MIT image reconstruction exhibits non-linearity and ill-posedness that cannot be treated with linear algorithms. We propose to implement for the first time in MIT two effective inversion methods known in non-linear optimization as Levenberg Marquardt (LMM) and Powell's Dog Leg (PDLM) methods. These methods employ damping and trust region techniques for controlling convergence and improving minimization of the objective function. An adaptive version of Gauss Newton is also presented (AGNM), which implements a damping mechanism to the regularization parameter. Here, the level of penalty is varied during the iterative process. As a comparison between the methods, different criteria are examined from image reconstructions using the LMM, PDLM and AGNM. For test examples, volumetric image reconstruction of a perturbation within homogeneous cylindrical background is considered. For inversion, an independent finite element FEM software package Maxwell by Ansys is employed to generate simulated data using a model of a 16 channel MIT system. Numerical results are employed to show different performance characteristics between the methods based on convergence, stability and sensitivity to the choice of the regularization parameter. To demonstrate the effect of scalability of absolute imaging in MIT for more realistic problems, a human head model with an internal anomaly is used to produce reconstructions for different finer resolutions. AGNM is adopted here and employs the Krylov subspace method to replace the computationally demanding direct inversion of the regularized Hessian.

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“…Some alternative inverse methods are required to resolve the limited memory issue [19,20]. In [21], the CG method has been proposed for the large scale inversion of the electrical impedance tomography (EIT), however the Jacobian matrix needs to be loaded into computer memory.…”

Section: Inverse Problemmentioning

confidence: 99%

Three-Dimensional Magnetic Induction Tomography Imaging Using a Matrix Free Krylov Subspace Inversion Algorithm

Wei¹,

Soleimani²

2012

PIER

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Abstract-Magnetic induction tomography (MIT) attempts to image the passive electromagnetic properties (PEP) of an object by measuring the mutual inductances between pairs of coils placed around its periphery. In recent years, there has been an increase in applications of non-contact magnetic induction tomography. When finite element-based reconstruction methods are used, that rely on the inversion of a derivative operator, the large size of the Jacobian matrix poses a challenge since the explicit formulation and storage of the Jacobian matrix could be in general not feasible. This problem is aggravated further in applications for example when the number of coils is increased and in three-dimension. Krylov subspace methods such as conjugate gradient (CG) methods are suitable for such large scale inverse problems. However, these methods require use of the Jacobian matrix, which can be large scale. This paper presents a matrix-free reconstruction method, that addresses the problems of large scale inversion and reduces the computational cost and memory requirements for the reconstruction. The idea behind the matrixfree method is that information about the Jacobian matrix could be available through matrix times vector products so that the creation and storage of big matrices can be avoided. Furthermore the matrix vector multiplications were performed in multiple core fashion so that the computational time can decrease even further. The method was tested for the simulated and experimental data from lab experiments, and substantial benefits in computational times and memory requirements have been observed.

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

Cited by 54 publications

References 21 publications

The reconstruction problem

The reconstruction problem

Absolute Imaging of Low Conductivity Material Distributions Using Nonlinear Reconstruction Methods in Magnetic Induction Tomography

Three-Dimensional Magnetic Induction Tomography Imaging Using a Matrix Free Krylov Subspace Inversion Algorithm

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