A level set method for inverse problems

This paper is devoted to the solution of shape re onstru tion problems by a level set method. The basi motivation for the setup of this level set algorithm is the well-studied method of asymptoti regularization, whi h has been developed for ill-posed problems in Hilbert spa es. Using analogies to this method, the onvergen e analysis of the proposed level set method is established, it is shown that the evolving level set onverges to a solution in the symmetri dieren e metri as the arti ial time evolves to innity. Fur-thermore, the regularizing properties of the level set method are shown, if the dis repan y prin iple is used as a stopping rule. The numeri al implementation of the level set method is dis ussed and applied to some examples in order to ompare the numeri al results with theoreti al statements. The numeri al results demonstrate the power of the level-set, in parti ular for examples where the number of onne ted omponents the solution onsists of is not known a-priorly