Gompertz-driven kernel anisotropic diffusion for effective image denoising and semantic information preservation

Anisotropic diffusion remains widely used for image denoising because it preserves image details while achieving high perceptual and objective quality. However, its performance depends on the divergence term, which governs the diffusion process. This study embeds a modified Gompertz-driven kernel into the divergence term of an anisotropic diffusion formulation. The Gompertz function, known for its robust performance in inverse problems, such as electrical capacitance tomography and tumor growth modeling, is particularly effective in handling outliers and noise in time series data. Our empirical results demonstrate the effectiveness of this function in promoting noise removal and preserving critical image features, including edges and contours. Compared with classical methods, our formulation generates quality images with competitive peak signal-to-noise ratio, structural similarity, and mean squared error values. Notably, our method offers high stability, producing visually appealing images even at higher iteration counts. Embracing transparency and repeatability of our work, implementation source codes and datasets have been shared at https://github.com/bmaiseli/Anisotropic-Diffusion .