A medical image enhancement based on generalized class of fractional partial differential equations

Abstract

Background: The interest in using fractional calculus operators has grown in the field of image processing.Image enhancement is one of image processing tools that aims to improve the details of an image. The enhancement of medical images is a challenging task due to the unforeseeable variation in the quality of the captured images. 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.

Mathematical model based on fractional trace operator for COVID-19 image enhancement

“…Jalab et al (FITE) ( Jalab et al, 2021b,c ) introduced a new fractional integral entropy (FITE) for medical image improvement. Ibrahim et al (FPDE) ( Ibrahim Rabha et al, 2021 ), proposed a new class of fractional partial differential equations for medical image improvement using a similar approach.…”

“…3 The comparative analysis of enhancement results. (a) Input Image, (b) LFE ( Al-Shamasneh et al, 2018 ), (c) RF ( Raghunandan et al, 2017 ), (d) DIE ( Zhang et al, 2019 ), (e)FITE ( Jalab et al, 2021b,c ), (f) FPDE ( Ibrahim Rabha et al, 2021 ), (g) Proposed FToRE. …”

“…Recently, ( Ibrahim Rabha et al, 2021 ) presented a fractional partial differential equations(FPDEs) based mathematical model for medical image enhancement. The FPDE's key benefit is its ability to improve low-contrast photos.…”

“…This model well enhanced the input images using the image contents linked with the fractional power to enhance the illumination pixel value of the image. While, in Ibrahim et al ( Ibrahim Rabha et al, 2021 ), a new class of fractional partial differential equations (FPDEs) was presented for medical image enhancement. The achieved results showed the benefit of using FPDEs in improving the medical image quality.…”

“…Different image processing algorithms for image enhancement are developed for image contrast enhancement. The applications of fractional calculus in science, and engineering, have been significantly increased due to the ability of fractional calculus in obtaining accurate solutions which makes the fractional-order-based methods more suitable approaches for many image processing methods like image enhancement ( Ibrahim Rabha et al, 2021 , Jalab et al, 2021a , Jalab et al, 2017 ).…”