PDE-based hyperbolic-parabolic model for image denoising with forward-backward diffusivity

Document Type : Research Paper


Department of Mathematics, School of Basic Sciences and Research, Sharda University Greater Noida-201310, UP, India.


In the present study, we propose an effective nonlinear anisotropic diffusion-based hyperbolic parabolic model for image denoising and edge detection. The hyperbolicparabolic model employs a second-order PDEs and has a second-time derivative to time t. This approach is very effective to preserve sharper edges and better-denoised images of noisy images. Our model is well-posed and it has a unique weak solution under certain conditions, which is obtained by using an iterative finite difference explicit scheme. The results are obtained in terms of peak signal to noise ratio (PSNR) as a metric, using an explicit scheme with forward-backward diffusivities.