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<p>We propose a new variational framework to remove complex Cauchy noise from natural images. This framework is based on a image decomposition technique where an optimal texture is computed through a PDE-constrained optimization procedure. Since Cauchy noise affect seriously the smooth part of the image, a fractional-order operator is then introduced to restore it as well as possible. Furthermore, a new alternating direction method of multipliers (ADMM) is then applied to resolve the nonsmooth optimization problems involving nonlinear operators between function space with an evolutionary PDE. Denoising tests confirm that the proposed approach leads in general to a satisfactory recovered clean image when compared to results of other competitive denoising methods.</p>

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A nonsmooth ADMM-based approach to fractional-constrained denoising problems with convergence analysis

  • 期刊论文

  • 发表日期：

    2025年11月27日

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  • Hssaine Oummi,
  • Lekbir Afraites,
  • Aissam Hadri,
  • Amine Laghrib

摘要

We propose a new variational framework to remove complex Cauchy noise from natural images. This framework is based on a image decomposition technique where an optimal texture is computed through a PDE-constrained optimization procedure. Since Cauchy noise affect seriously the smooth part of the image, a fractional-order operator is then introduced to restore it as well as possible. Furthermore, a new alternating direction method of multipliers (ADMM) is then applied to resolve the nonsmooth optimization problems involving nonlinear operators between function space with an evolutionary PDE. Denoising tests confirm that the proposed approach leads in general to a satisfactory recovered clean image when compared to results of other competitive denoising methods.