Nonlinear PDE Model for Image Restoration Using Second-Order Hyperbolic Equations

Abstract

In this article we consider a novel nonlinear PDE-based image denoising technique. The proposed restoration model uses second-order hyperbolic diffusion equations. It represents an improved nonlinear version of a linear hyperbolic PDE model developed recently by the author, providing more effective noise removal results while preserving the edges and other image features. A rigorous mathematical investigation is performed on this new differential model and its well-posedness is treated. Next, a consistent finite-difference numerical approximation scheme is proposed for this nonlinear diffusion-based approach. Our successful image denoising experiments and method comparisons are also described.

Keywords:

• Detail-preserving filtering
• Hyperbolic diffusion equation
• Image denoising and restoration
• Nonlinear PDE model
• Numerical discretization scheme
• Well-posedness investigation

Mathematics Subject Classification:

• 35-xx
• 35Lxx
• 65-xx
• 65Nxx
• 68-xx
• 68Uxx
• 68U10
• 94-xx
• 94A08

ACKNOWLEDGMENTS

We are very grateful to the reviewer and the editor of this journal for their suggestions and proposed corrections to improve the article.

Notes

Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/lnfa.