A semi-implicit binary level set method for source reconstruction problems

The aim of this paper is to investigate the application of a semi- implicit additive operator splitting scheme based binary level set method to source reconstruction problems. We reformulate the original model to be a new constrained optimization problem under the binary level set framework and solve it by the augmented Lagrangian method. Then we propose an efficient gradient-type algorithm based on the additive operator splitting scheme. The proposed algorithm can create new holes during the evolution. Topological changes can be handled automatically and complex geometry can be recovered under a certain amount of noise in the observation data. Numerical examples are presented to show the effectiveness and efficiency of our method.