A novel variable exponent PDE with dependency on γ(u,|∇u0,σ|) for image despeckling application

Within the realm of image processing, image denoising holds significant importance. This study focuses on tackling denoising challenges posed by Speckle noise. We introduce a novel variable $\gamma (u,|\nabla u_{0,\sigma }|)$-PDE-based denoising model, offering a fresh perspective. Our approach involves a unique class of PDEs, wherein the nonlinear structure relies on spatially nonlocal exponent dependent factors linked to the target solution and also its gradient. This innovation incorporates grayscale information by introducing the variable exponent $\gamma$, which controls much better the diffusion and incorporates information from wide regions. The existence and uniqueness of the proposed PDE are established through Galerkin’s approximation. Furthermore, a series of experiments are conducted for denoising, including comparisons with other models, in order to validate the selection of the variable exponent parameter. This research contributes to the advancement of image denoising methods with high theoretical foundations and potential implications for other applications.