Ibrahim Rabha W, Jalab Hamid A, Karim Faten Khalid, Alabdulkreem Eatedal, Ayub Mohamad Nizam
Institute of Electrical and Electronics Engineers (IEEE: 94086547), Kuala Lumpur, Malaysia.
Department of Computer System and Technology, Faculty of Computer Science and Information Technology, Universiti Malaya, Kuala Lumpur, Malaysia.
Quant Imaging Med Surg. 2022 Jan;12(1):172-183. doi: 10.21037/qims-21-15.
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.
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.
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.
Overall, this model significantly improves the details of the given datasets, and could potentially help the medical staff during the diagnosis process.
在图像处理领域，对使用分数阶微积分算子的兴趣与日俱增。图像增强是旨在改善图像细节的图像处理工具之一。由于所采集图像质量存在不可预见的变化，医学图像增强是一项具有挑战性的任务。
在本研究中，我们提出了一种基于分数阶偏微分方程（FPDEs）类别的数学模型。该类别由比例 - 卡普托混合算子（PCHO）构成。此外，单位圆盘中几何函数的一些性质被用于确定此类FPDEs的上界解。上界解以广义超几何函数的关系表示。FPDE的主要优势在于其能够通过所提出的分数阶增强算子增强低对比度强度。
所提出的图像增强算法针对不同质量的脑部和肺部计算机断层扫描（CT）数据集进行了测试，结果表明它具有鲁棒性，能够承受质量上的显著变化。对于脑部磁共振成像（MRI）图像，Brisque、Piqe、SSEQ和SAMGVG的定量结果分别为40.93%、41.13%、66.09%和31.04%，对于CT肺部图像，相应结果分别为39.07、41.33、30.97和159.24。比较结果表明，所提出的图像增强模型实现了最佳的图像质量评估。
总体而言，该模型显著改善了给定数据集的细节，并可能在诊断过程中对医务人员有所帮助。
