Image Restoration with a New Class of Forward-Backward-Forward Diffusion Equations of Perona-Malik Type with Applications to Satellite Image Enhancement

A new class of anisotropic diffusion models is proposed for image processing which can either be viewed as a novel kind of regularization of the classical Perona-Malik model or, as it is advocated by the authors, as a new independent model. The models are diffusive in nature and are characterized by the presence of both forward and backward regimes. In contrast to the Perona-Malik model, in the proposed model the backward regime is confined to a bounded region and gradients are only allowed to grow up to large but tunable size thus effectively preventing indiscriminate singularity formation, i.e. staircasing. Extensive numerical experiments demonstrate that the method is a viable denoising/deblurring tool. The method is significantly faster than competing state-of-theart methods and appears to be particularly effective for simultaneous denoising and deblurring (cf. Section 4.1). An application to satellite image enhancement is also presented.