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<p>In this paper, we introduce a variational image decomposition model based on non-local total variation and formulated through a Nash equilibrium framework. The proposed method aims to separate a noisy image into two distinct components: a structural part <i>u</i>, representing the main geometric features of the image, and a texture component <i>v</i>, capturing fine-scale oscillations and details. This decomposition is achieved by minimizing two coupled energy functionals corresponding to each component, leading to a stable Nash equilibrium. The integration of non-local operators enables the model to exploit self-similarities in natural images, ensuring effective noise reduction while preserving structural integrity. Experimental results on standard test images demonstrate that the proposed approach achieves superior separation quality compared to classical methods, particularly under high noise conditions.</p>

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Image decomposition based on non local operator via Nash game equilibrium for noise removal

  • 期刊论文

  • 发表日期：

    2026年3月9日

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  • Requia Addouch,
  • Noureddine Moussaid,
  • Omar Gouasnouane,
  • Anouar Ben-Loghfyry

摘要

In this paper, we introduce a variational image decomposition model based on non-local total variation and formulated through a Nash equilibrium framework. The proposed method aims to separate a noisy image into two distinct components: a structural part u, representing the main geometric features of the image, and a texture component v, capturing fine-scale oscillations and details. This decomposition is achieved by minimizing two coupled energy functionals corresponding to each component, leading to a stable Nash equilibrium. The integration of non-local operators enables the model to exploit self-similarities in natural images, ensuring effective noise reduction while preserving structural integrity. Experimental results on standard test images demonstrate that the proposed approach achieves superior separation quality compared to classical methods, particularly under high noise conditions.