A Fast Iterative Shrinkage-Thresholding Algorithm for Electrical Resistance Tomography

摘要

Image reconstruction in Electrical Resistance Tomography (ERT) is an ill-posed nonlinear inverse problem. Considering the influence of the sparse measurement data on the quality of the reconstructed image, the l_1 regularized least-squares program (l_1 regularized LSP), which can be cast as a second order cone programming problem, is introduced to solve the inverse problem in this paper. A normally used method of implementing the l_1 regularized LSP is based on the interior point method whose main drawback is the relatively slow convergence speed. To meet the need of high speed in ERT, the fast iterative shrinkage-thresholding algorithm (FISTA) is employed for image reconstruction in our work. Simulation results of the FISTA and l1_ls algorithm show that the l_1 regularized LSP is superior to the l_2 regularization method, especially in avoiding the over-smoothing of the reconstructed image. In addition, to improve the convergence speed and imaging quality in FISTA algorithm, the initial guess is calculated with the conjugate gradient method. Comparative simulation results demonstrate the feasibility of FISTA in ERT system and its advantage over the l1_ls regularization method.