Solution of the inverse problem of magnetic induction tomography (MIT)

Abstract

Magnetic induction tomography (MIT) of biological tissue is used to reconstruct the changes in the complex conductivity distribution inside an object under investigation. The measurement principle is based on determining the perturbation DeltaB of a primary alternating magnetic field B0, which is coupled from an array of excitation coils to the object under investigation. The corresponding voltages DeltaV and V0 induced in a receiver coil carry the information about the passive electrical properties (i.e. conductivity, permittivity and permeability). The reconstruction of the conductivity distribution requires the solution of a 3D inverse eddy current problem. As in EIT the inverse problem is ill-posed and on this account some regularization scheme has to be applied. We developed an inverse solver based on the Gauss-Newton-one-step method for differential imaging, and we implemented and tested four different regularization schemes: the first and second approaches employ a classical smoothness criterion using the unit matrix and a differential matrix of first order as the regularization matrix. The third method is based on variance uniformization, and the fourth method is based on the truncated singular value decomposition. Reconstructions were carried out with synthetic measurement data generated with a spherical perturbation at different locations within a conducting cylinder. Data were generated on a different mesh and 1% random noise was added. The model contained 16 excitation coils and 32 receiver coils which could be combined pairwise to give 16 planar gradiometers. With 32 receiver coils all regularization methods yield fairly good 3D-images of the modelled changes of the conductivity distribution, and prove the feasibility of difference imaging with MIT. The reconstructed perturbations appear at the right location, and their size is in the expected range. With 16 planar gradiometers an additional spurious feature appears mirrored with respect to the median plane with negative sign. This demonstrates that a symmetrical arrangement with one ring of planar gradiometers cannot distinguish between a positive conductivity change at the true location and a negative conductivity change at the mirrored location.

Application of expectation maximization algorithm in magnetic induction tomography

“…Tikhonov regularization algorithm Tikhonov regularization algorithm [14] is to minimize the objective function defined by (13) where V m refers to the measured voltage value and F(σ) is the voltage vector which is calculated by solving the forward problem. The regularization parameter is used to control the size of the penalty term, which is required to stabilize the iteration [15].…”

Four Dimensional Reconstruction Using Magnetic Induction Tomography: Experimental Study

“…In the literature, MIT have been extensively studied in 2D and most of the systems are still producing low resolution 2D imaging result [3,4,[7][8][9][10], which focuses on the cross sectional distribution and assumes there is no axial (z-axis) conductivity variation. For some applications where the axial conductivity change is significant, this assumption is unrealistic and the 2D imaging is no longer applicable.…”

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

“…To date, the major progress reported in MIT image reconstruction mainly involved the application of linear algorithms including single step schemes such as linear back-projection [3,4], Tikhonov regularization [5][6][7][8][9][10], truncated singular value decomposition (TSVD) [9], and iterative schemes like simultaneous iterative reconstruction technique (SIRT) [9], Landweber method [11] and the conjugate gradients least squares (CGLS) method [12]. Single step reconstruction methods are fast but they can only produce qualitative images.…”