Image restoration and classification by topological asymptotic expansion

We present in this paper a new way for modeling and solving image restoration and classification problems, 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 restored or classified at the first iteration of the optimization process. Moreover, the computational cost of this iteration is reduced drastically using spectral methods. We also propose an algorithm which provides the optimal classes (number and values) for the unsupervised regularized classification problem.