A Couple of Novel Image Enhancement Methods Depending on the Prabhakar Fractional Approaches

Abstract

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.