Stable denoising-enhancement of images by telegraph-diffusion operators

The recently-proposed family of Telegraph-Diffusion (TeD) operators is analyzed in the context of image enhancement. Stability of such schemes in terms of energy convergence is investigated and compared with that of the widely-used diffusion-based schemes, thereby resolving the Perona-Malik paradox. The results indicating stability are further generalized in the context of the Forward-and-Backward (FAB) TeD enhancement operator. An approximated version of the enhancement operator that offers an increased stability is proposed and examined. This scheme is implemented in both stable and unstable regimes of the original FAB-TeD operator and shown to yield results similar to those obtained by the latter, without losing stability. The theoretical conclusions regarding stability of the approximated FAB-TeD are reinforced by simulations, exhibiting enhanced images with sharpened edges and yet very limited compromise on the quality of other image details.