A couple of novel image enhancement methods depending on the Prabhakar fractional approaches

Integrating fractional calculus into image processing techniques offers a useful and robust approach. In this study, we proposed contrast enhancement filters using Prabhakar fractional integral operator based on Grunwald–Letnikov and forward Euler. We evaluated the performance of the proposed enhancement methods on both high and low contrast images and compared them with fractional and non-fractional contrast enhancement methods. To demonstrate the superiority of our methods, we employed five different image quality metrics: PSNR, MSE, SSIM, FSIM, and entropy. For low contrast images, our methods not only achieved acceptable results for each metric—PSNR values above 25, SSIM values above 0.9, MSE values below 200, FSIM values above 0.97, and entropy values above 7—but also demonstrated better performance compared to other methods. In high contrast images, despite an overall decline in metric scores, the Grunwald–Letnikov based method remains the leading approach among both fractional and non-fractional methods. Additionally, empirical results provide evidence that the proposed methods are more effective in enhancing low contrast images compared to high contrast images.