可变阶次分数阶微分实现图像自适应增强

为了改善图像增强的效果，提出了一种可变阶次的分数阶微分图像自适应增强算子.该算子的数学原理是根据图像的局部统计信息和结构特征来动态调整分数阶微分的阶次.在图像增强的过程中，分数阶微分的阶次满足在图像“强边缘”处具有较大的微分阶次，在图像“弱边缘”或纹理处具有较小的微分阶次，在图像平滑处具有微小的微分阶次，在判断为噪声处具有负阶次.建立了图像增强效果和分数阶微分阶次之间的非线性量化关系，构造了相应的自适应函数，实现了图像的自适应增强.实验结果表明，在无噪声的情况下，该方法较传统的分数阶微分算子在图像增强方面效果更好；在有噪声的情况下，该方法具有一定的噪声免疫能力.

Realization of adaptive image enhancement with variable fractional order differential

In order to improve the effect of image enhancement,an adaptive image enhancement operator with variable fractional order differential was proposed.The mathematical theory of the operator was that the order of fractional order differential was dynamically adjusted according to the local statistical information and structural features of images.In the process of image enhancement,the order of fractional order differential should be larger in the strong edge region of the image,smaller in the weak edge or texture regions of the image,and jerkwater in the smooth region of the image.In particular,the order of fractional order differential should be negative in the judged noise region.The nonlinear quantitative relationship between image enhancement effect and order of fractional order differential was established,and the corresponding adaptive function was constructed to realize the adaptive enhancement of image.The experimental results show that the proposed method exhibits better image enhancement effect compared with the traditional fractional order differential operator in the noise-free case,and has certain noise immunity in the noise case.