Updating preconditioners for nonlinear deblurring and denoising image restoration

Image restoration is the recovery of images that have been degraded by blur and noise. Nonlinear degenerate diffusion partial differential equation models for image restoration require often the solution of a challenging discrete problem. We consider solving the related discrete models in the time-scale steps by Krylov iterative solvers accelerated by updating a preconditioner based on incomplete factorizations which presents a global computational cost slightly more than linear in the number of the image pixels. We demonstrate the efficiency of the strategy by denoising and deblurring some images with a generalized Alvarez–Lions–Morel-like partial differential equation model discretized by a semi implicit complementary volume scheme.