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In this paper, we present a stable, reliable and robust method for reconstructing a three dimensional density function from a set of two dimensional electric tomographic images. By minimizing an energy functional consisting of a fidelity term and a regularization term, an L  2 -gradient flow is derived. The flow is integrated by a finite element method in the spatial direction and an explicit Euler scheme in temporal direction. The experimental results show that the proposed method is efficient and effective.

Operator Splitting for the Non-stationary Thermal Convection Problems