| [1] | MANDELBROT B B. The Fractal Geometry of Nature[M]. New York: W. H. Freeman and Company, 1983. |
| [2] | AZARANG A and GHASSEMIAN H. Application of fractional-order differentiation in multispectral image fusion[J]. Remote Sensing Letters, 2017, 9(1): 91–100. doi: 10.1080/2150704X.2017.1395963 |
| [3] | LI Bo and XIE Wei. Adaptive fractional differential approach and its application to medical image enhancement[J]. Computers & Electrical Engineering, 2015, 45: 324–335. doi: 10.1016/j.compeleceng.2015.02.013 |
| [4] | BAI Jian and FENG Xiangchu. Fractional-order anisotropic diffusion for image denoising[J]. IEEE Transactions on Image Processing, 2007, 16(10): 2492–2502. doi: 10.1109/TIP.2007.904971 |
| [5] | HU Fuyuan, SI Shaohui, WONG H S, et al. An adaptive approach for texture enhancement based on a fractional differential operator with non-integer step and order[J]. Neurocomputing, 2015, 158: 295–306. doi: 10.1016/j.neucom.2014.10.013 |
| [6] | HE Ning, WANG Jinbao, ZHANG Lulu, et al. An improved fractional-order differentiation model for image denoising[J]. Signal Processing, 2015, 112: 180–188. doi: 10.1016/j.sigpro.2014.08.025 |
| [7] | YUAN Jianjun and LIU Lipei. Anisotropic diffusion model based on a new diffusion coefficient and fractional order differential for image denoising[J]. International Journal of Image and Graphics, 2016, 16(1): 1650003. doi: 10.1142/S0219467816500030 |
| [8] | JALAB H A, IBRAHIM R W, and AHMED A. Image denoising algorithm based on the convolution of fractional Tsallis entropy with the Riesz fractional derivative[J]. Neural Computing and Applications, 2017, 28(S1): 217–223. doi: 10.1007/s00521-016-2331-7 |
| [9] | PU Yifei, ZHOU Jiliu, and YUAN Xiao. Fractional differential mask: A fractional differential-based approach for multiscale texture enhancement[J]. IEEE Transactions on Image Processing, 2010, 19(2): 491–511. doi: 10.1109/TIP.2009.2035980 |
| [10] | PU Yifei, SIARRY P, CHATTERJEE A, et al. A fractional-order variational framework for retinex: Fractional-order partial differential equation-based formulation for multi-scale nonlocal contrast enhancement with texture preserving[J]. IEEE Transactions on Image Processing, 2018, 27(3): 1214–1229. doi: 10.1109/TIP.2017.2779601 |
| [11] | 牛为华, 孟建良, 崔克彬, 等. 利用Grümwald-Letnikov分数阶方向导数的图像增强方法[J]. 计算机辅助设计与图形学学报, 2016, 28(1): 129–137. doi: 10.3969/j.issn.1003-9775.2016.01.016 NIU Weihua, MENG Jianliang, CUI Kebin, et al. Image enhancement method using grümwald -letnikov fractional directional differential[J]. Journal of Computer-Aided Design &Computer Graphics, 2016, 28(1): 129–137. doi: 10.3969/j.issn.1003-9775.2016.01.016 |
| [12] | GAO Caobang, ZHOU Jiliu, HU Jingrong, et al. Edge detection of colour image based on quaternion fractional differential[J]. IET Image Processing, 2011, 5(3): 261–272. doi: 10.1049/iet-ipr.2009.0409 |
| [13] | 李博, 谢巍. 基于自适应分数阶微积分的图像去噪与增强算法[J]. 系统工程与电子技术, 2016, 38(1): 185–192. doi: 10.3969/j.issn.1001-506X.2016.01.29 LI Bo and XIE Wei. Image enhancement and denoising algorithms based on adaptive fractional differential and integral[J]. Systems Engineering and Electronics, 2016, 38(1): 185–192. doi: 10.3969/j.issn.1001-506X.2016.01.29 |
| [14] | 陈庆利, 黄果, 门涛, 等. 数字图像的局部分数阶微分增强[J]. 四川大学学报: 工程科学版, 2016, 48(4): 115–122. doi: 10.15961/j.jsuese.2016.04.016 CHEN Qingli, HUANG Guo, MEN Tao, et al. Local fractional differential algorithm for image enhancement[J]. Journal of Sichuan University:Engineering Science Edition, 2016, 48(4): 115–122. doi: 10.15961/j.jsuese.2016.04.016 |
| [15] | 姒绍辉, 胡伏原, 付保川, 等. 自适应非整数步长的分数阶微分掩模的图像纹理增强算法[J]. 计算机辅助设计与图形学学报, 2014, 26(9): 1438–1449. SI Shaohui, HU Fuyuan, FU Baochuan, et al. An algorithm for texture enhancement based on fractional differential mask using adaptive non-integer step[J]. Journal of Computer-Aided Design &Computer Graphics, 2014, 26(9): 1438–1449. |
| [16] | ZHAO Mengdan, GAO Xuzhen, PAN Yue, et al. Image encryption based on fractal-structured phase mask in fractional Fourier transform domain[J]. Journal of Optics, 2018, 20(4): 045703. doi: 10.1088/2040-8986/aab247 |