中文摘要：

提出了一种数字图像的0～1阶分数阶微分增强模板。）,kRiemann-Liouville分数阶积分定义出发推导出0-1阶Riemann-Liouville分数阶微分方程及其离散化方程；构造了x轴负方向、x轴正方向、y轴负方向、滞正方向、左下对角、左上对角、右下对角、右上对角8个相互中心对称方向的分数阶微分模板，并讨论了这8个方向分数阶微分模板的数值运算规则；讨论图像的熵和微分阶次之间的关系，并根据熵值最终确定使图像增强效果最好的微分阶次。实验表明能比较明显地增强图像的纹理和边缘细节，增强后的图像清晰度提高，图像视觉效果明显；对高斯平滑后的图像的增强效果也十分明显。

英文摘要：

An image enhancement algorithm based on 0-1 order Riemann-Liouville fractional differential is presented in this paper. The Riemann-Liouville differential equation and its discretization form are deduced from the Riemann-Liouville definition. According to the discretization equation, the structures and parameters of eight fractional differential masks are constructed respectively. The numerical implementation algorithms of the eight differential masks are discussed too. Finally, the relationships between the entropies of enhanced images with the orders are discussed, then, the most optimal order is obtained. The computer experiments show that the algorithm has excellent feedback for nonlinearly enhancing the textural details of the digital image and it can obviously enhance texture details and edges, the enhanced images have markedly visual effect enhance capabilities of the Gaussian smoothed images are also obvious too.