Improved Primal-Dual Interior-Point Method Using the Lawson-Norm for Inverse Problems

Abstract

Electrical impedance tomography (EIT), geophysics and undersea target reconstruction are typical non-linear ill-posed inverse problems, and in many cases, the anomalous bodies feature with a clear boundary. Thus, it is suitable to obtain sharp boundaries and blocky features with the Total Variation (TV) functional regularization. However, the TV function regularization leads to a non-differentiable objective function at zero in the inverse formulation and reduces the algorithm robustness. In this paper, we propose an improved primal-dual interior-point method (PD-IPM) based on the Lawson norm to get sharp spatial profiles of the anomalous bodies. Furthermore, the impact of the smooth parameter is investigated to get the inverse results. Numerical experiment using simulated data is setup to support our claim.