Multi-Phase Permittivity Reconstruction in Electrical Capacitance Tomography by Level-Set Methods

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In this article, the numerical methods of reconstructing the permittivity profile of multi-phase material flow from data collected in electrical capacitance tomography (ECT) are presented. Under the assumption that multi-phase permittivity distributions are piecewise-constant functions, we develop iterative reconstruction algorithms by level-set methods that provide estimates for the interfaces and permittivity values simultaneously. Our formulation is based on the minimization of a functional consisting of a least-squares data fitting term and a regularization term. The regularization is by weighted arc lengths of the interfaces with weights determined by the permittivity differences across the interfaces. From the Euler--Lagrange equations, interface evolution equations are set up based on a variational level-set method, and a linear system is derived to update the unknown permittivity values within the iteration process. Numerical examples are presented to illustrate the effectiveness of the reconstruction algorithms on two- and three-phase material flows.



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