A class of elliptic systems with discontinuous variable exponents and L1 data for image denoising

Publication date: December 2019Source: Nonlinear Analysis: Real World Applications, Volume 50Author(s): Dazhi Zhang, Kehan Shi, Zhichang Guo, Boying WuAbstractThis 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,N3}, where p−≔essinfx∈Ωp(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 L1 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.

Source: Nonlinear Analysis: Real World Applications - June 4, 2019 Category: Research Source Type: research