Application of Fractional Integral Model in Construction of Image Enhancement Mask

Abstract

— Image enhancement is crucial in image processing applications to improve visual quality for better interpretation and analysis. Conventional enhancement techniques that rely on integer-order operators frequently have trouble striking a balance between feature retention and noise reduction. In this work, we propose a 5 × 5 and 7 × 7 fractional-order mask using the Caputo fractional integral, which offers a more flexible and accurate approach to image enhancement. To evaluate the effectiveness of the proposed approach, Gaussian noise is added to test images and the enhancement performance is quantitatively assessed using the Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index Measure (SSIM). The experimental results demonstrate that the proposed fractional integral masks effectively enhance image quality by improving texture visibility and edge details while reducing noise. In particular, as the fractional order approaches one, the enhanced images show significant improvement in both PSNR and SSIM values, indicating better structural preservation and visual fidelity. These results confirm that the proposed Caputo fractional integral-based mask provides a flexible and effective alternative for image enhancement.