Newton Method for Shape Reconstruction of a burried Scatterer

A Newton method for reconstruction of the shape of the perfectly electrical conducting (PEC) object located inside arbitrary shaped dielectric cylinder through the measured far-field scattering data is given. The scattered field is represented as a single-layer potential which leads to an ill-posed integral equation of the first kind that is solved via Tikhonov regularization. The presented Newton based method combines ideas of both the iterative and decomposition methods and inherits the advantages of each of them, such as getting good reconstructions and not requiring a forward solver at each step. The numerical results show that the method yields good reconstruction.