An approach for solving inverse problems involving obstacles is proposed. The approach uses a level-set method which has been shown to be effective in treating problems of moving boundaries, particularly those that involve topological changes in the geometry. We develop two computational methods based on this idea. One method results in a nonlinear time-dependant partial differential equation for the level-set 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.