Kernel-based fourth-order diffusion for image noise removal

Abstract

The fourth-order partial differential equations have good performance on noise smoothing and edge preservation without creating blocky effects on smooth regions. However, for low signal-to-noise ratio images, the discrimination between edges and noise is a challenging problem. A novel kernel-based fourth-order diffusion is proposed in this paper. It introduces a kernelized gradient operator in the fourth-order diffusion process, which leads to more effective noise removal capability. Experiment results show that this method outperforms several previous anisotropic diffusion methods for noise removal and edge preservation.

Keywords:

• diffusion
• image filter
• Kernel method
• noise removal
• anisotropic

2010 AMS Subject Classifications::

• 68U10
• 94A08
• 30C40
• 60G35
• 60J60

Acknowledgements

The authors would like to thank the anonymous referees for their valuable comments and suggestions, which actually stimulated this work. This work was supported by the National Natural Science Foundation of China [Grant Nos. 61201297, 11101320 and 11201362].