Existence and uniqueness for electrode models for electric current computed tomography
SIAM Journal on Applied Mathematics
Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Electrical Impedance Tomography
SIAM Review
Computational Methods for Inverse Problems
Computational Methods for Inverse Problems
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We present numerical methods of reconstructing permittivity profile of material flow from data collected in electrical capacitance tomography (ECT). Based on a formula for the sensitivity maps from a partial differential equation model, we propose a unified framework of iterative algorithms using updated sensitivity maps to properly incorporate the non-linear nature of the problem and a regularization mechanism to address the ill-posedness. For two- and three-phase flows, the total variation (TV) regularization method is shown to be effective in reconstructing the permittivity profiles accurately in a few iterations, without any a priori knowledge of the unknown permittivity values.