Stable Image Enhancement by Adaptive Damped Wave Equation with Force Term

The recently-proposed family of Forward-and-Backward (FAB) Telegraph-Diffusion (TeD) equations [5] are analyzed in the context of enhancement image processing schemes. Stability of such schemes is investigated in terms of energy convergence. A more stable approximated version of the enhancement operator is proposed and examined. This new 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 the other image details.