Fast Multilevel Algorithm for a Minimization Problem in Impulse Noise Removal

An effective 2-phase method for removing impulse noise was recently proposed. Its phase 1 identifies noisy pixel candidates by using median-type filters. Then in phase 2, it restores only the noisy pixel candidates by some variational methods. The resulting method can handle salt-and-pepper noise and random-valued impulse noise of noise level as high as 90% and 60% respectively. The aim of this paper is to generalize a fast multilevel method for Gaussian denoising to solving the minimization problem arising in phase 2 of the 2-phase method. The multilevel algorithm gives better images than standard optimization method such as the Newton method or conjugate gradient method. Also it can handle more general regularization functionals than the smooth ones previously considered. Supporting numerical experiments on 2D gray scale images are presented. AMS subject class: 68U10, 65F10, 65K10.