Nonlocal total variation system for the restoration of textured images

ABSTRACT

A new nonlocal total variation reaction–diffusion system is proposed, analysed and implemented for image denoising. In the way, it is obtained by analysing the case where $p\to 1$ in the nonlocal p-Laplacian reaction–diffusion system proposed in [F. Karami, D. Meskine, and K. Sadik, A new nonlocal model for the restoration of textured images, J. Appl. Anal. Comput. 9(6) (2019), pp. 2070–2095.]. We established the existence and uniqueness of the proposed model. Numerical and comparatives experiments are presented that illustrate the main features of the new model and that demonstrate its effectiveness as a denoising tool.

Keywords:

• Image denoising
• nonlocal TV system
• textured images

2010 Mathematics Subject Classifications:

• Primary: 35K92
• 35K57
• Secondary:68R01

Disclosure statement

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