Signal and image enhancement by a generalized forward-and-backward adaptive diffusion process

Signal and image enhancement in the presence of noise is considered in the context of the scale-space approach. A modified dynamic process, based on the action of an adaptive diffusion equation, is presented. The nonlinear diffusion coefficient is locally adjusted according to image features such as edges, textures and moments, and, as such, can also reverse its sign, i.e. switches from a forward to a backward (inverse) diffusion process according to a given set of criteria. This results in a generalized forward-and-backward adaptive diffusion process that enhances features such as transients and singularities in the one-dimensional case, and edges in images, while locally denoising smoother segments of the signal or image. Advantages afforded by the generalized adaptive diffusion process are illustrated by examples of both one-dimensional signals and images.