Reconstruct permeability of heterogeneous body using T-Ω 3-D formulation and Gauss-Newton´s method with total variation regularization

In the inverse problems several techniques are used, in particular induced currents techniques. In spite of their complexities, a diversity of fields, such as imaging, use these techniques. Owing to the fact that it is not a direct problem, several conditions must be joined together to give satisfactory results. The choice of the Model, the Numerical Technique, the Iterative Method and the choice of Regularization Method are the factors which influence the exactitude and the convergence of the results. In this paper, we are going to determine a permeability distribution of heterogeneous body, from a nondestructive evaluation signal, using the numerical approach. We will solve the forward solution with a three-Dimensional T-Ω formulation of Finite Element Method in order to determine the magnetic field, and a Gauss-Newton algorithm with Total Variation Regularization to solve and stabilize the solution resulting from the optimisation problem. The permeability of the object is assumed to be linear and isotropic. Results for the permeability imaging will be reconstructed using synthetically generated data.