Scholarlink

<p>This work presents a novel coupled PDE-based model designed for multiframe image super-resolution, combining a variable <i>p</i>(<i>x</i>)-Laplace operator, a fractional Laplacian, and a Caputo time fractional derivative. The model offers a unified approach to enhance image resolution while addressing noise reduction, edge preservation, and texture fidelity. The <i>p</i>(<i>x</i>)-Laplace operator adapts diffusion dynamics to spatial variations, the fractional Laplacian ensures smoothness without sacrificing details, and the Caputo derivative introduces memory effects to better capture temporal dependencies across frames. We rigorously analyze the model’s well-posedness using the Faedo–Galerkin method and fixed-point techniques to establish the existence and uniqueness of weak solutions. An adaptive numerical scheme is developed to implement the model, and extensive experiments are conducted on synthetic and real-world multiframe low-resolution datasets. These experiments, which include various noise levels and degradation processes, demonstrate the model’s robustness and superior performance in reconstructing high-resolution images. Comparisons with existing methods highlight the efficiency of the proposed approach in delivering sharper, more accurate results, making it a promising tool for super-resolution and advanced image processing tasks.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Enhanced Image Super-Resolution via a Coupled Fractional Caputo Derivative and Adaptive p(x)-Laplacian Model

  • 期刊论文

  • 发表日期：

    2026年1月7日

查看全文
  • Z. Zaabouli,
  • K. Jenkal,
  • L. Afraites,
  • A. Laghrib

摘要

This work presents a novel coupled PDE-based model designed for multiframe image super-resolution, combining a variable p(x)-Laplace operator, a fractional Laplacian, and a Caputo time fractional derivative. The model offers a unified approach to enhance image resolution while addressing noise reduction, edge preservation, and texture fidelity. The p(x)-Laplace operator adapts diffusion dynamics to spatial variations, the fractional Laplacian ensures smoothness without sacrificing details, and the Caputo derivative introduces memory effects to better capture temporal dependencies across frames. We rigorously analyze the model’s well-posedness using the Faedo–Galerkin method and fixed-point techniques to establish the existence and uniqueness of weak solutions. An adaptive numerical scheme is developed to implement the model, and extensive experiments are conducted on synthetic and real-world multiframe low-resolution datasets. These experiments, which include various noise levels and degradation processes, demonstrate the model’s robustness and superior performance in reconstructing high-resolution images. Comparisons with existing methods highlight the efficiency of the proposed approach in delivering sharper, more accurate results, making it a promising tool for super-resolution and advanced image processing tasks.