A novel algorithm based on L1-Lp norm for inverse problem of electromagnetic tomography

Abstract

Electromagnetic tomography (EMT) is a novel imaging modality of electrical tomography, which appears to be very promising. The precision and imaging speed of image reconstruction algorithms of EMT are the keys to its application in industrial and biomedical fields. Image reconstruction in EMT is a typical ill-posed and ill-conditioned inverse problem. Following analyzing the advantages and disadvantages of traditional Tikhonov regularization algorithm and total variation algorithm, a new objective functional is introduced with L1 norm on the data term and Lp norm on the regularization term in this paper, which transforms the inverse problem of EMT into an optimization problem. Besides, the L1-Lp optimization framework is solved by the approximation Gauss-Newton algorithm. Both numerical simulation and experimental results demonstrate that the proposed algorithm is capable of enhancing spatial resolution. It also proves that the proposed algorithm has better performance in terms of the typical patterns, compared with the traditional image reconstruction algorithms such as linear back projection (LBP), standard Tikhonov regularization algorithm and the projected Landweber iterative algorithm.