An adaptive anisotropic diffusion model integrating total variation and non-local means for image denoising

Xiaojuan Zhang; Xiaojuan Zhang

doi:10.3934/math.20251240

AIMS Mathematics

2025, Volume 10, Issue 12: 28207-28220. doi: 10.3934/math.20251240

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Research article

An adaptive anisotropic diffusion model integrating total variation and non-local means for image denoising

Xiaojuan Zhang ^,

School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou, 450046, China

Received: 28 July 2025 Revised: 02 November 2025 Accepted: 20 November 2025 Published: 01 December 2025
MSC : 35K25, 35K61, 68U10

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.
- total variation,
- non-local means,
- image denoising,
- weak solution
Citation: Xiaojuan Zhang. An adaptive anisotropic diffusion model integrating total variation and non-local means for image denoising[J]. AIMS Mathematics, 2025, 10(12): 28207-28220. doi: 10.3934/math.20251240

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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.

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