A class of elliptic systems with discontinuous variable exponents and L1 data for image denoising. (December 2019) - Zhang, Dazhi; Shi, Kehan; Guo, Zhichang; Wu, Boying
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.