Quantitative Reconstruction of the Exterior Boundary Shape of Metallic Inclusions Using Electrical Capacitance Tomography

Electrical capacitance tomography (ECT) is a non-intrusive technology to image the permittivity distribution from capacitance measurements on periphery. Recent studies demonstrated that ECT can also be used to image metallic samples. A shape-based approach to reconstruct metallic inclusions quantitatively by ECT is presented, which incorporates information on the materials systematically. The formula to calculate the Jacobian is deduced with concise derivations. To deal with the problem that the traditional Tikhonov regularization method does not possess the immunity to generate deep concavities or the ability to escape from the situation, a penalty on the curvature is introduced. The penalty pushes the partial curves with deep concavities outward to gain more sensitivity. The performance of reconstructing metallic inclusions from numerical and practical measurements demonstrates the advantage of the presented algorithm in preventing deep concavities and achieving an overall approximation of the inclusions.