SIGMOIDAL APPROXIMATIONS FOR SELF-INTERACTING LINE PROCESSES IN EDGE-PRESERVING IMAGE-RESTORATION

Image restoration is formulated as the problem of minimizing a non-con vex cost function E(f, I) in which a binary self-interacting line proc ess is introduced. Each line element is then approximated by a sigmoid al function of the local intensity gradient, which depends on a parame ter T, thus obtaining a sequence of functions F-T(f) converging to a f unction F(f) that implicitly refers to the line process. In the case o f a non-interacting line process, function F(f) coincides with the one derived for the weak membrane problem. The minimum of F(f) is compute d through a GNC-type algorithm which minimizes in sequence the various F-T(f)'s using gradient descent techniques. When generalized to the c ase of self-interacting line elements, the method is flexible in intro ducing any kind of constraint on the configurations of the discontinui ty field. The results of simulations highlight that the method improve s the quality of the reconstruction when constraints on the line proce ss are introduced, without any increase in the computational costs wit h respect to the case where there are no self-interactions between lin es.