A class of elliptic systems with discontinuous variable exponents and L1 data for image denoising. (December 2019)

• Record Type: Journal Article
• Authors: Zhang, Dazhi; Shi, Kehan; Guo, Zhichang; Wu, Boying
• Is Part Of: Nonlinear analysis. Volume 50(2019)
• Page Start: 448
• Page End: 468
• Publication Date: 2019-12
• Subjects: Elliptic system -- Discontinuous variable exponent -- L1 data -- Image denoising; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2019.05.012
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: This paper investigates a class of elliptic systems consisting of the p ( x ) -Laplacian equation and the Poisson equation for image denoising. Under the assumption that p − > max { 1, N 3 }, where p − ≔ ess inf x ∈ Ω p ( x ) and N is the dimension of Ω, we prove the existence and uniqueness of weak solutions for the homogeneous Neumann boundary value problem with discontinuous variable exponent p ( x ) and L 1 data. The proof, which is based on Schauder's fixed-point theorem, also provides an iterative scheme for solving the system numerically. Experimental results illustrate that the proposed system with piecewise constant p ( x ) performs better than commonly used smooth p ( x ) in image denoising.