An adaptive anisotropic diffusion model integrating total variation and non-local means for image denoising
Xiaojuan Zhang · AIMS Mathematics · 2025
This study proposes an adaptive diffusion equation for noise removal that combines total variation (TV) and non-local means (NL-means). By incorporating a weighted non-local data fidelity term, the model adaptively switches between TV and NL-means based on image features. A key advantage of this approach is its ability to correct over-smoothed low-contrast areas, minimize residual noise near edges, and reduce staircasing artifacts during denoising. Furthermore, the existence of a weak solution for the proposed model is rigorously established.