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Magnetic detection electrical impedance tomography (MDEIT) is an imaging modality that aims to compute the cross-sectional distribution of the conductivity of a volume from the magnetic flux density surrounding the object. Owing to the Biot-Savart law, the MDEIT inverse problem is inherently ill-conditioned making image reconstruction highly susceptible to the effects of noise and numerical errors. Appropriate priors or penalties are needed to facilitate reconstruction and to restrict the search space to a specific solution set. The images have the sparsity property and sharp variations. Consequently, this paper presents an approach involving a combination of the L¹ and total variation norm penalties, the former to suppress spurious background signals and enforce sparsity and the latter to preserve local smoothness and piecewise constancy in the MDEIT reconstructed images. The primal dual-interior point method (PD-IPM) for minimizing the joint L¹--TV penalty was used in the paper. The method was validated by using MDEIT simulated data and experimental data in comparison with the performances of the L², L¹ and total variation norm penalty-based approaches. The results show that the joint L¹--TV regularized algorithm preserves sparsity property, local smoothness and piecewise constancy, leading to improvements in the localization of the reconstructed images in MDEIT. [ABSTRACT FROM AUTHOR]

Magnetic detection electrical impedance tomography (MDEIT) is an imaging modality that aims to reconstruct the cross-sectional conductivity distribution of a volume from the magnetic flux density surrounding an object. The MDEIT inverse problem is inherently ill-posed, necessitating the use of regularization. The most commonly used L² norm regularizations generate the minimum energy solution, which blurs the sharp variations of the reconstructed image. Consequently, this paper presents the total variation (TV) regularization to preserve discontinuities and piecewise constancy of the MDEIT reconstructed image. The primal dual-interior point method (PD-IPM) is employed for minimizing the TV penalty in this paper. The proposed method is validated by MDEIT simulated data. In comparison with the performance of L² norm regularization, the results show that TV regularized algorithm produces sharper images and has better robustness to noise. The TV regularized algorithm preserves local smoothness and piecewise constancy, leading to improvements in the localization of the reconstructed conductivity images in MDEIT. [ABSTRACT FROM AUTHOR]