Image Restoration via Nonstandard Diffusion

We present a functional of nonstandard growth for which the corresponding minimization problem provides a model for image denoising, enhancement, and restoration. The diffusion resulting from the proposed model is a combination of isotropic and anisotropic diffusion. Isotropic diffusion is used at locations with low gradient and total variation based diffusion is used along likely edges. At all other locations, the type of anisotropy varies according to the local image information. Experimental results illustrate the effectiveness of the model in removing noise and retaining sharp edges while avoiding the ’staircasing effect’. Existence and uniqueness of the proposed model are also established.