Single-Step 3-D Image Reconstruction in Magnetic Induction Tomography: Theoretical Limits of Spatial Resolution and Contrast to Noise Ratio

Abstract

Abstract-Magnetic induction tomography (MIT) is a lowresolution imaging modality for reconstructing the changes of the complex conductivity in an object. MIT is based on determining the perturbation of an alternating magnetic field, which is coupled from several excitation coils to the object. The conductivity distribution is reconstructed from the corresponding voltage changes induced in several receiver coils. Potential medical applications comprise the continuous, non-invasive monitoring of tissue alterations which are reflected in the change of the conductivity, e.g. edema, ventilation disorders, wound healing and ischemic processes. MIT requires the solution of an ill-posed inverse eddy current problem. A linearized version of this problem was solved for 16 excitation coils and 32 receiver coils with a model of two spherical perturbations within a cylindrical phantom. The method was tested with simulated measurement data. Images were reconstructed with a regularized single-step GaussNewton approach. Theoretical limits for spatial resolution and contrast/noise ratio were calculated and compared with the empirical results from a Monte-Carlo study. The conductivity perturbations inside a homogeneous cylinder were localized for a SNR between 44 and 64 dB. The results prove the feasibility of difference imaging with MIT and give some quantitative data on the limitations of the method.

Single-coil magnetic induction tomographic three-dimensional imaging

“…8,9 Some authors have indicated a desire to reduce the number of coils, with one approach calling for the repositioning of either the coils in the array or the object itself. 10 Whether MIT uses many or few coils, improved imaging calls for as many measurements as possible.…”

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

“…Given the current iterate σ k , the step d needed to obtain the next iterate σ k+1 can be calculated by the regularized Gauss Newton method using the system of Equation (6). Alternatively, it can also be evaluated via the steepest descent method using (4), where the step factor α can be computed via the relation given by:…”

“…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.…”

Modified Conjugate Gradient Algorithm and its Convergence for Electromagnetic Tomography

“…Electromagnetic Tomography ( EMT ) is a noninvasive and contactless imaging modality based on law of electromagnetic induction, which aims to reconstruct the electrical conductivity distribution of the object field [1][2][3][4][5][6][7][8] .A sinusoidal time-varying magnetic field is generated by excitation coils and the changes within the object field due to conductivity perturbation are recorded by receiver coils. EMT, like EIT(electrical impedance tomography) and ECT (electrical capacitance tomography) is a 'soft-field' technique where the relation between measurements of receiver and conductivity distribution in object field is nonlinear, which can linear…”