Mathematical modeling and numerical analysis of diffusion processes in image processing

This paper introduces a new image enhancement technique based on a revised diffusion model that aims to balance between the reduction of noise and preservation of edges.The new model uses adaptive parameters and sophisticated numerical methods to overcome the shortcomings of conventional image processing techniques. This study aims to develop and apply a diffusion model with critical parameters such as the diffusion coefficient, sensitivity parameter, and edge-stopping function parameter. Performance of the model is tested using experiments, comparing with conventional Gaussian smoothing and the Perona-Malik model. Experimental results confirm that the extended diffusion model outperforms the conventional methods on peak signal-to-noise ratio and structural similarity index. The model greatly enhances noise reduction when the parameters are set optimally while preserving significant image details.