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<p>Image processing is a fundamental operation in many scientific and engineering fields, where it often becomes necessary to remove noise to enhance quality and subsequently extract features in pixelated data. In this paper, we develop a new denoising method based on the Ψ-Hilfer Fractional Regularized Perona–Malik Diffusion equation, combined with the Adams–Bashforth–Moulton Predictor-Corrector (ABM-PECE) numerical scheme. The fractional Ψ-Hilfer operator permits a more flexible control of diffusion rates and the balance between edge preservation and smoothing, whereas the regularized term stabilizes the solution, maintaining descent without the staircase effects typical of more conventional diffusion methods for image processing. We apply our Ψ-Hilfer version to a series of benchmark test images of various qualities against additive noise to determine its denoising effectiveness. Ultimately, results show that our method gains significantly improved PSNR and SSIM values from its original Perona–Malik model and even the fractional ones, proving that Ψ-Hilfer fractional diffusion outperforms existing diffusion-based image denoising methods reported in the literature.</p>

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Enhancing Image Denoising Performance Using Ψ-Hilfer Fractional Regularized Perona–Malik Diffusion

  • 期刊论文

  • 发表日期：

    2026年4月7日

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  • A. Y. Xani

摘要

Image processing is a fundamental operation in many scientific and engineering fields, where it often becomes necessary to remove noise to enhance quality and subsequently extract features in pixelated data. In this paper, we develop a new denoising method based on the Ψ-Hilfer Fractional Regularized Perona–Malik Diffusion equation, combined with the Adams–Bashforth–Moulton Predictor-Corrector (ABM-PECE) numerical scheme. The fractional Ψ-Hilfer operator permits a more flexible control of diffusion rates and the balance between edge preservation and smoothing, whereas the regularized term stabilizes the solution, maintaining descent without the staircase effects typical of more conventional diffusion methods for image processing. We apply our Ψ-Hilfer version to a series of benchmark test images of various qualities against additive noise to determine its denoising effectiveness. Ultimately, results show that our method gains significantly improved PSNR and SSIM values from its original Perona–Malik model and even the fractional ones, proving that Ψ-Hilfer fractional diffusion outperforms existing diffusion-based image denoising methods reported in the literature.