Title: Weak solutions for a class of generalised image restoration models

Authors: Shuaijie Li; Peng Li

Addresses: School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, P.R. China ' School of Mathematics and Statistics Science, Ludong University, YanTai, ShanDong 264025, P.R. China

Abstract: In this paper, based on some well-known restoration models, first, we propose a general form of image restoration functional model under some conditions, and get a class of related nonlinear parabolic partial differential equations. Second, we have established the existence and uniqueness of weak solutions for these equations. This work has supplied theoretical basis for image restoration models, and has great significance in image restoration field.

Keywords: anisotropic diffusion; approximate solution; existence; image restoration; isotropic diffusion; nonlinear diffusion; parabolic PDE; ROF model; total variation; uniqueness; weak solution.

DOI: 10.1504/IJDSDE.2018.092665

International Journal of Dynamical Systems and Differential Equations, 2018 Vol.8 No.3, pp.190 - 203

Received: 18 Oct 2016
Accepted: 19 Jun 2017
Published online: 27 Jun 2018 *

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