Methods: In this study, we present a mathematical model based on the class of fractional partial differential equations (FPDEs). The class is formulated by the proportional-Caputo hybrid operator (PCHO). Moreover, some properties of the geometric functions in the unit disk are applied to determine the upper bound solutions for this class of FPDEs. The upper bound solution is indicated in the relations of the general hypergeometric functions. The main advantage of FPDE lies in its capability to enhance the low contrast intensities through the proposed fractional enhanced operator.
Results: The proposed image enhancement algorithm is tested against brain and lungs computed tomography (CT) scans datasets of different qualities to show that it is robust and can withstand dramatic variations in quality. The quantitative results of Brisque, Piqe, SSEQ, and SAMGVG were 40.93%, 41.13%, 66.09%, and 31.04%, respectively for brain magnetic resonance imaging (MRI) images and 39.07, 41.33, 30.97, and 159.24 respectively for the CT lungs images. The comparative results show that the proposed image enhancement model achieves the best image quality assessments.
Conclusions: Overall, this model significantly improves the details of the given datasets, and could potentially help the medical staff during the diagnosis process.