A variable exponent nonlocal p(x)-Laplacian equation for image restoration

In this paper, we focus on the mathematical and numerical study of a variable exponent nonlocal $p\left(X\right)$-Laplacian equation for image denoising. Based on the Semigroup Theory, we prove the existence and uniqueness of solution for the proposed model. To illustrate the efficiency and effectiveness of our model, we provide the denoising experimental results as well we compare it with some existing models in the literature.