Image processing by topological asymptotic analysis

We present in this paper a new way for modeling and solving image processing problems (restoration, classification,...), the topological gradient method. This method is considered in the frame of variational approaches and the minimization of potential energy with respect to conductivity. The numerical experiments show the efficiency of the topological gradient approach. The image is most of the time processed at the first iteration of the optimization process. Moreover, the computational cost of this iteration is reduced drastically using spectral methods.