An image-enhancement method based on variable-order fractional differential operators

In this study, we develop a new algorithm based on fractional operators of variable-order in order to enhance image quality. First, three kinds of popular high-order discrete formulas are adopted to obtain the coefficients, and subsequently, a mask optimization method for selecting the fractional order adaptively is applied to construct a variable-order fractional differential mask along with the coefficients generated from the first step. We carry out experiments on OCT thoracic aorta images and some nature images with low contrast and noise, demonstrating that the high-order discrete method leads to significantly better performance in enhancing the edge information nonlinearly compared to the standard first-order discrete method. Moreover, the optimized mask with variable-order of the fractional derivative not only can preserve the edge information of the processed images adequately, but it also effectively suppresses the noise in the smooth area.