We propose a new algorithm for computing regularized solutions to inverse problems where the unknown functions is a characteristic function and where the forward operator is linear. Our approach can be seen as an alternative to the level-set method and is based on an efficient computation of minimizers for a Tikhonov functional...
Keywords: inverse problem, interface problem, regularization, thresholding, bounded variation, exact relaxation, surrogate functional, level set method, topological derivative
07/2007 | Journal of Inverse and Ill-posed Problems, Walter de Gruyter