Impedance imaging with first-order TV regularization

EIT problem is a typical inverse problem with serious ill-posedness. In general, regularization techniques are necessary for such ill-posed inverse problems. To overcome ill-posedness, the total variation (TV) regularization is widely used and it is also successfully applied to EIT. For realtime monitoring, a fast and robust image reconstruction algorithm is required. By exploiting recent advances in optimization, we propose a first-order TV algorithm for EIT, which simply consists of matrix-vector multiplications and in which the sparse structure of the system can be easily exploited. Furthermore, a typical smoothing parameter to overcome nondifferentibility of the TV term is not needed and a closed form solution can be applied in part using soft thresholding. It shows a fast reconstruction in the beginning. Numerical experiments using simulated data and real experimental data support our claim.