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Absolute conductivity reconstruction in magnetic induction tomography using a nonlinear method.

Manuchehr Soleimani1, William R B Lionheart

  • 1M. Soleimani is with the William Lee Innovation Center, School of Materials, The University of Manchester, Manchester UK.

IEEE Transactions on Medical Imaging
|December 16, 2006
PubMed
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Magnetic induction tomography (MIT) images electrical properties using impedance data. A nonlinear, regularized Gauss-Newton algorithm with an efficient Jacobian formula enables stable imaging, even with noisy data.

Area of Science:

  • Electromagnetism
  • Computational Imaging
  • Applied Physics

Background:

  • Magnetic induction tomography (MIT) aims to image target electrical and magnetic properties.
  • The inverse eddy current problem is nonlinear and ill-posed, necessitating regularization for stable solutions.

Purpose of the Study:

  • To implement and evaluate a regularized Gauss-Newton algorithm for solving the nonlinear inverse eddy current problem in MIT.
  • To derive and utilize an efficient adjoint field formula for calculating the Jacobian matrix.

Main Methods:

  • An edge-based finite element method (A, V formulation) was used to solve the forward problem.
  • A regularized Gauss-Newton algorithm was employed as the iterative inverse solver.
  • An adjoint field formula was derived for efficient Jacobian computation.

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Main Results:

  • The derived Jacobian formula efficiently calculates conductivity perturbations using electric field inner products.
  • Sensitivity maps were shown to vary significantly with conductivity changes, confirming the need for nonlinear algorithms.
  • The inverse solver's performance was evaluated using simulated, noisy data.

Conclusions:

  • The regularized Gauss-Newton algorithm provides a stable and effective method for MIT.
  • The efficient Jacobian calculation is crucial for the performance of the nonlinear reconstruction algorithm.
  • The study highlights the importance of nonlinear approaches in MIT due to changing sensitivity maps.