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<p>This paper investigates a class of degenerate forward–backward diffusion equations with a nonlinear source term, proposed as a model for removing multiplicative noise in images. Based on Rothe’s method, the relaxation theorem, and Schauder’s fixed-point theorem, we establish the existence of Young measure solutions for the corresponding initial boundary problem. The continuous dependence result relies on the independence property satisfied by the Young measure solution. Numerical experiments illustrate the denoising effectiveness of our model compared to other denoising models.</p>

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A class of forward–backward diffusion equations for multiplicative noise removal

  • 期刊论文

  • 发表日期：

    2025年8月20日

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  • Yihui Tong,
  • Wenjie Liu,
  • Zhichang Guo,
  • Wenjuan Yao

摘要

This paper investigates a class of degenerate forward–backward diffusion equations with a nonlinear source term, proposed as a model for removing multiplicative noise in images. Based on Rothe’s method, the relaxation theorem, and Schauder’s fixed-point theorem, we establish the existence of Young measure solutions for the corresponding initial boundary problem. The continuous dependence result relies on the independence property satisfied by the Young measure solution. Numerical experiments illustrate the denoising effectiveness of our model compared to other denoising models.