A level-set approach for inverse problems involving obstacles

An approach for solving inverse problems involving obstacles is proposed. The approach uses a levelset method which has been shown to be effective in treating problems of moving boundaries, particu larly those that involve topological changes in the geometry. We develop two computational methods based on this idea. One method results in a nonlinear time-dependent partial differential equation for the levelset function whose evolution minimizes the residual in the data fit. The second method is an optimization that generates a sequence of level set functions that reduces the residual. The methods are illustrated in two applications: a deconvolution problem and a diffraction screen reconstruction problem.