Sparse reconstruction of EMT based on compressed sensing and Lp regularization with the split Bregman method

Abstract

Electromagnetic tomography (EMT) is a promising tomographic method used to reconstruct the conductivity and permeability material owing to its contactless nature. However, the EMT inverse problem is ill-posed due to the soft-field characteristic and limited prior information, which will severely affect the imaging quality. To address the challenge, a novel sparse reconstruction algorithm is proposed in this article on the basis of compressed sensing (CS) and Lp regularization. The EMT inverse problem is converted into the L1 norm regularization problem using the advantages of the compressed sensing theory. To combine the merits of L1 and L2 regularization, Lp regularization is deployed as the regularizer taking the place of L1 norm, which can overcome the over-smoothing and over-sparsity of the reconstruction objects. A modified split Bregman (SB) method is exploited to effectively cope with the Lp regularization problem. An accelerating method is further applied to improve the reconstruction speed. The sensitivity matrix calculation is performed by the perturbation method. Simulation studies are implemented to show the superiority of the presented method in comparison with the classical methods. The effectiveness of the proposed method is further validated by the developed EMT system. Experimental results confirm that the proposed method has better imaging capability, which provides a great candidate for the practical application of EMT.