Hybrid variable exponent model for image denoising: A nonstandard high-order PDE approach with local and nonlocal coupling

Abstract

In this paper, we propose a novel hybrid model combining local and nonlocal methods for effective image denoising. The model utilizes variable exponents p(x) to achieve adaptive diffusion behavior and preserve image features. Nevertheless, the coupling structure of our proposed process, along with the spatial dependence of p(x), poses challenges in theoretical analysis. To address this, we investigate the existence and uniqueness of the solution using the Faedo-Galerkin approximation, a priori estimates, and compactness considerations. Through these theoretical investigations, we demonstrate the existence of a weak solution for the coupled parabolic system. Overall, our model outperforms existing methods in noise reduction and image quality preservation.