A nonlinear primal-dual method for total variation-based image restoration

We present a new method for solving total variation (TV) minimization probl ems in image restoration. The main idea is to remove some of the singularit y caused by the nondifferentiability of the quantity \del u\ in the definit ion of the TV-norm before we apply a linearization technique such as Newton 's method. This is accomplished by introducing an additional variable for t he flux quantity appearing in the gradient of the objective function, which can be interpreted as the normal vector to the level sets of the image u. Our method can be viewed as a primal-dual method as proposed by Conn and Ov erton [A Primal-Dual Interior Point Method for Minimizing a Sum of Euclidea n Norms, preprint, 1994] and Andersen [Ph.D. thesis, Odense University, Den mark, 1995] for the minimization of a sum of Euclidean norms. In addition t o possessing local quadratic convergence, experimental results show that th e new method seems to be globally convergent.