An improved noise removal model based on nonlinear fourth-order partial differential equations

Abstract

In this paper, we propose an improved noise removal model based on a nonlinear fourth-order partial differential equation (PDE). It associates with the minimization of a certain energy subject to spatially varying constraints involving local variance measures. We discuss the existence and uniqueness of the solutions for the proposed model. The main advantage of the proposed method over the related methods is that it can not only preserve textures but also avoid the staircase effect in smooth regions in the process of denoising. Experimental results illustrate advantages of our proposed method in visual improvement as well as an increase in the signal-to-noise ratio over related PDE methods.

Keywords:

• image restoration
• noise removal
• variation
• fourth-order partial differential equations
• nonlinear filtering

2010 AMS Subject Classifications:

• 68U10
• 58E30
• 49K20

Acknowledgments

The authors would like to thank the Editor-in-Chief, Prof. Abdul Khaliq, and the referees for their valuable comments and suggestions which improved the present work to a great extend.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Major Program of the National Natural Science Foundation of China [Grant No. 41390454] and the National Science and Technology Major Project [Grant Nos. 2011ZX05023-005-009 and 2011ZX05044]. This research is also partly supported by Beijing Center for Mathematics and Information Interdisciplinary Science (BCMIIS).