Application of the topological gradient to image restoration and edge detection

We show in this paper that the emerging topological gradient method is a new way for modelling and solving image restoration problems. This method is considered in the frame of variational diffusive approaches for the minimization of potential energy with respect to conductivity. The numerical experiments show the efficiency of the topological gradient approach. The image is restored at the first iteration of the optimization process. Moreover, the computational cost of this iteration is reduced drastically using spectral methods.