Convergence of an iterative method for variational deconvolution and impulsive noise removal

Image restoration, i.e., the recovery of images that have been degraded by blur and noise, is a challenging inverse problem. A unified variational approach to edge-preserving image deconvolution and impulsive noise removal has recently been suggested by the authors and shown to be effective. It leads to a minimization problem that is iteratively solved by alternate minimization for both the recovered image and the discontinuity set. The variational formulation yields a nonlinear integro-differential equation. This equation was linearized by fixed point iteration. In this paper, we analyze and prove the convergence of the iterative method.