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

• In this paper, we apply the lp regularization method to the ERT inverse problem. For the method has a non-quadratic constraints which leads to a nonlinear equation, it is hard to solve. To overcome the difficulty, we add a surrogate term in the objective function. Then we use a Landweber-type iterative that involve a denoising procedure at each iteration step and provides a sequence of approximations converging in norm to the variational minimizer.
• We discuss the selection strategy of the parameters.
• Simulations were carried out to evaluate the performance of the different ways.The simulation results demonstrate the feasibility of the iterative thresholded algorithm.

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 l2 regularization penalty term by weighted lp(1≤p<2)lp(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 lp(1≤p<2)lp(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 l2 regularization method, the proposed algorithms can produce images of higher quality, which are evaluated both qualitatively and quantitatively.