论文信息 - Stable Image Enhancement by Adaptive Damped Wave Equation with Force Term

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.

Yehoshua Y. Zeevi | Vadim Ratner

[1] Jitendra Malik,et al. Scale-Space and Edge Detection Using Anisotropic Diffusion , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[2] Yehoshua Y. Zeevi,et al. Forward-and-backward diffusion processes for adaptive image enhancement and denoising , 2002, IEEE Trans. Image Process..

[3] Mitsuhiro Nakao,et al. Decay and Global Existence for Nonlinear Wave Equations with Localized Dissipations in General Exterior Domains , 2005 .

[4] Joshua Kiddy K. Asamoah,et al. Fractal–fractional age-structure study of omicron SARS-CoV-2 variant transmission dynamics , 2022, Partial Differential Equations in Applied Mathematics.

[5] Yehoshua Y. Zeevi,et al. Enhancement of Textured Images Using Complex Diffusion Incorporating Schrodinger's Potential , 2006, 2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings.

[6] Yehoshua Y. Zeevi,et al. Denoising-Enhancing Images on Elastic Manifolds , 2011, IEEE Transactions on Image Processing.

[7] Joachim Weickert,et al. Theoretical Foundations for Discrete Forward-and-Backward Diffusion Filtering , 2009, SSVM.