(untitled) (Journal of Computational Mathematics, 2018)
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.