@article{Zhang2025, 
author = {Xiaojuan Zhang},
title = {An adaptive anisotropic diffusion model integrating total variation and non-local means for image denoising},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {12},
pages = {28207-28220},
keywords = {total variation, non-local means, image denoising, weak solution},
url = {https://www.sciopen.com/article/10.3934/math.20251240},
doi = {10.3934/math.20251240},
abstract = {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.}
}