IRWIN AND JOAN JACOBS CENTER FOR COMMUNICATION AND INFORMATION TECHNOLOGIES Stable Image Enhancement by Approximated Forward-and- Backward Wave Equation

The recently-proposed family of Forward-andBackward (FAB) Telegraph-Diffusion (TeD) equations [9] is analyzed in the context of image enhancement. Stability of such schemes in terms of energy convergence is investigated. 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 similar results 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.