A convex relaxation method for computing exact global solutions for multiplicative noise removal

We propose a convex relaxation technique for computing global solutions for the nonconvex multiplicative noise model. The method is based on functional lifting by introducing an additional dimension. We employ a primal–dual-based gradient-type algorithm in numerical implementations to overcome the nondifferentiability of the total variation term. Numerical results show that our algorithm is highly efficient. Furthermore, global solutions of the original model can be obtained with no dependence on the initial guess.