An iterative thresholding algorithm for the inverse problem of electrical resistance tomography

摘要

Image reconstruction in Electrical Resistance Tomography (ERT) is an ill-posed nonlinear inverse problem. Considering the sparsity property of ERT model, in this paper, we replace the conventional l_2 regularization penalty term by weighted l_p(1 ≤ p < 2) penalty term. To overcome the non-quadratic property, a surrogate term is added to the objective function. An interesting condition is that the classical methods (e.g. SVD, Landweber iteration) can be used to solve the l_p(1 ≤ p < 2) least squares problems. Both typical and complicated distributions (e.g. annular and cross-shape) have been examined using a 16-electrode configuration based on the finite element method (FEM) software COMSOL. The simulated results demonstrate the feasibility of the proposed algorithm, and compared to the l_2 regularization method, the proposed algorithms can produce images of higher quality, which are evaluated both qualitatively and quantitatively.