Fractional diffusion equation-based image denoising model using CN–GL scheme

ABSTRACT

In recent decades, variational methods have achieved great success in reducing noise owing to the use of total variation (TV). The TV-based denoising model introduced by Rudin–Osher–Fatemi (ROF) is playing vital role in denoising the different types of images. In this paper, a new denoising model based on space fractional diffusion equation is proposed with a finite domain discretized using effective applications of Crank–Nicholson and Grünwald Letnikov difference schemes. The ROF model has been adopted to solve the proposed model with the help of Alternative Direction Implicit method to denoise the image. The experimental results of the proposed model have been compared with those of the Gaussian model and it is observed that the Peak Signal-to-Noise Ratio has been improved.

KEYWORDS:

• Space-fractional partial derivatives
• Crank–Nicholson
• Grünwald Letnikov
• Rudin–Osher–Fatemi model
• image denoising

2010 AMS SUBJECT CLASSIFICATIONS:

• 68U10
• 35R11

Acknowledgements

The authors would like to thank the referees for their careful reading, critical comments and helpful suggestions, which helped to improve the quality of this article.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The second author was supported by the University Grants Commission, New Delhi, INDIA under Special Assistance Programme F.510/7/DRS-1/2016(SAP-I).