Anisotropic selective inverse diffusion for signal enhancement in the presence of noise

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 a nonlinear diffusion equation, is presented. The diffusion coefficient is adjusted according to the local gradient, intensity and other image properties, and as such also reverses its sign, i.e. switches from a forward to a backward (inverse) diffusion process according to a given criterion. This results in enhancement of transients and singularities in the one-dimensional case, and of edges in images, while locally denoising smoother segments of the signal or image. Regularization of the ill-posed inverse diffusion problem is discussed. Examples of both one-dimensional signals and images are presented.