A Newton method to reconstruct the shapeof a buried sound soft object through the measured far-fieldscattering data is given. The scattered field is representedas a single-layer potential which leads to an ill-posed integralequation of the first kind that is solved via Tikhonov regular-ization. The presented Newton based method combines ideasof both the iterative and decomposition methods and inheritsthe advantages of each of them, such as getting good recon-structions and not requiring a forward solver at each step.The numerical results show that the method yields good re-construction.
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