Abstract—A novel fourth-order Partial Differential Equation (PDE) - based image restoration technique is proposed in this work. It is based on a well-posed fourth order nonlinear diffusion based model with some properly chosen boundary conditions, which is combined to a two dimensional filter kernel. An explicit iterative finite difference method based numerical approximation algorithm is then constructed for solving the PDE model. It is stable and converges fast to the solution of the differential model, which represents the recovered image. The proposed filtering approach removes successfully the additive noise, overcome the unintended effects, such as the blurring and staircasing, and preserves successfully the edges and other image details. As it results from the obtained method comparison results, this approach outperforms not only the classic 2D image filters that often generate the undesired blurring effect, but also some nonlinear second order partial differential equation based smoothing schemes that produce the blocky effect.
Index Terms—image denoising and restoration, fourth-order PDE model, nonlinear diffusion, additive Gaussian noise, finite difference method, numerical approximation scheme
Cite: Tudor Barbu, "Detail-Preserving Fourth-Order Nonlinear PDE-Based Image Restoration Framework," Journal of Image and Graphics, Vol. 8, No. 1, pp. 5-8, March 2020. doi: 10.18178/joig.8.1.5-8
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