Total Variation Regularization With Split Bregman-Based Method in Magnetic Induction Tomography Using Experimental Data

Abstract

Magnetic induction tomography (MIT) is an imaging modality with a wide range of potential applications due to its non-contact nature. MIT is a member of the electrical tomography family that faces the most difficult imaging challenges, due to its demanding measurement accuracy requirements and its difficult forward and inverse problems. This paper presents for the first time split Bregman total variation (TV) regularization to solve the MIT inverse problem. Comparative evaluations are presented between proposed TV algorithm and more commonly used Tikhonov regularization method. Tikhonov regularization, which is based on the ${l}_{2}{-norm}$ , is solved linearly, while TV is solved using the split Bregman formulation, which has been shown to be optimal for ${l}_{1}{-norm}$ regularization. Experimental results are quantified by a number of image quality measurements, which show the superiority of the proposed TV method both on low conductivity and high conductivity MIT data. Significant improvement in MIT imaging results will make the proposed TV method a great candidate for both types of MIT imaging.