NEWTON'S METHOD FOR INVERSE OBSTACLE SCATTERING OF BURIED OBJECTS

A Newton method to reconstruct the shape of a buried sound soft object 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.