A novel method for the numerical solution of a hybrid inverse problem of electrical conductivity imaging

A novel method for the numerical solution of a hybrid (coupled physics) inverse problem is proposed. Based on a regularized weighted mean curvature flow equation, this method can be considered as an alternative to the variational approach to solving weighted least gradient Dirichlet problems arising in electrical conductivity imaging, in particular, in Current Density Impedance Imaging (CDII). Utilizing the Sternberg-Ziemer arguments, convergence of regularized solutions to a unique function of weighted least gradient is established. The numerical convergence study is also conducted to demonstrate the computational effectiveness of the proposed method.