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MONTE: The Method of Nonflat Time Evolution in PDE-based Image Restoration

This article is concerned with effective numerical techniques for partial differential equation (PDE)based image restoration. Numerical realizations of most PDE-based denoising models show a common drawback: loss of fine structures. In order to overcome the drawback, the article introduces a new timestepping procedure, called the method of nonflat time evolution (MONTE), in which the timestep size is determined based on local image characteristics such as the curvature or the diffusion magnitude. The MONTE provides the PDE-based restoration models with an effective mechanism for the equalization of the net diffusion over a wide range of image frequency components. It can be easily applied to diverse evolutionary PDE-based restoration models and their spatial and temporal discretizations. It has been numerically verified that the MONTE results in a significant reduction in nonphysical dissipation and preserves fine structures such as edges and textures satisfactorily, while it removes the noise with an improved efficiency. Various numerical results are shown to confirm the claim.