[
[1] Mathieu, B., Melchior, P., Oustaloup, A., Ceyral, C. (2003). Fractional differentiation for edge detection. Signal Processing, 83 (11), 2421-2432.10.1016/S0165-1684(03)00194-4
]Search in Google Scholar
[
[2] Cuesta, E., Kirane, M., Malik, S.A. (2012). Image structure preserving denoising using generalized fractional time integrals. Signal Processing, 92 (2), 553-563.10.1016/j.sigpro.2011.09.001
]Search in Google Scholar
[
[3] Magin, R., Ortigueira, M.D., Podlubny, I., Trujillo, J. (2011). On the fractional signals and systems. Signal Processing, 91 (3), 350-371.10.1016/j.sigpro.2010.08.003
]Search in Google Scholar
[
[4] Li, Y.L., Ding, Y.Q., Li, T. (2016). Nonlinear diffusion filtering for peak-preserving smoothing of a spectrum signal. Chemometrics and Intelligent Laboratory Systems, 156, 157-165.10.1016/j.chemolab.2016.06.007
]Search in Google Scholar
[
[5] Witkin, A.P. (1983). Scale-space filtering. In Proceedings of the Eighth International Joint Conference on Artificial Intelligence, Volume 2. Morgan Kaufmann Publishers, 1019-1022.
]Search in Google Scholar
[
[6] Perona, P., Malik, J. (1990). Scale-space and edge detection using anisotropic diffusion. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12, 629-639.10.1109/34.56205
]Search in Google Scholar
[
[7] Alvarez, L., Lions, P.L., Morel, J. (1992). Image selective smoothing and edge detection by nonlinear diffusion. II. SIAM Journal on Numerical Analysis, 29 (3), 845-866.10.1137/0729052
]Search in Google Scholar
[
[8] Anagaw, A.Y., Sacchi, M.D. (2012). Edge-preserving seismic imaging using the total variation method. Journal of Geophysics and Engineering, 9, 138-146.10.1088/1742-2132/9/2/138
]Search in Google Scholar
[
[9] Barbu, T. (2014). Robust anisotropic diffusion scheme for image noise removal. Procedia Computer Science, 35, 522-530.10.1016/j.procs.2014.08.133
]Search in Google Scholar
[
[10] Barbu, T. (2015). Nonlinear PDE model for image restoration using second-order hyperbolic equations. Numerical Functional Analysis and Optimization, 36, 1375-1387.10.1080/01630563.2015.1066388
]Search in Google Scholar
[
[11] Droske, M., Bertozzi, A.L. (2010). Higher-order feature-preserving geometric regularization. SIAM Journal on Imaging Sciences, 3, 21-51.10.1137/090751694
]Search in Google Scholar
[
[12] Gerig, G., Kubler, O., Kikinis, R., Jolesz, F.A. (1992). Nonlinear anisotropic filtering of MRI data. IEEE Transactions on Medical Imaging, 11, 221-232.10.1109/42.14164618218376
]Search in Google Scholar
[
[13] Liang, Z., Liu, W., Yao, R. (2016). Contrast enhancement by nonlinear diffusion filtering. IEEE Transactions on Image Processing, 25, 673-686.10.1109/TIP.2015.250740526685234
]Search in Google Scholar
[
[14] Oussous, M.A., Alaa, N., Khouya, Y.A. (2014). Anisotropic and nonlinear diffusion applied to image enhancement and edge detection. Journal of Computer Applications in Technology, 49, 122-133.10.1504/IJCAT.2014.060523
]Search in Google Scholar
[
[15] Yu, J., Wang, Y. (2011). Image noise reduction based on anisotropic diffusion: A survey. Journal of Electronic Measurement and Instrument, 25, 105-116.10.3724/SP.J.1187.2011.00105
]Search in Google Scholar
[
[16] Michelgonzalez, E., Cho, M.H., Lee, S.Y. (2011). Geometric nonlinear diffusion filter and its application to X-ray imaging. Biomedical Engineering Online, 10, 47-47.10.1186/1475-925X-10-47312164321639933
]Search in Google Scholar
[
[17] Ma, W., You, Y., Kaveh, M. (2009). Image restoration regularized by a fourth order PDE. Proceedings of SPIE, 724509.
]Search in Google Scholar
[
[18] You, Y., Kaveh, M. (2000). Fourth-order partial differential equations for noise removal. IEEE Transactions on Image Processing, 9, 1723-1730.10.1109/83.86918418262911
]Search in Google Scholar
[
[19] Weickert, J. (1997). A review of nonlinear diffusion filtering. In Scale-Space Theory in Computer Vision. LNCS 1252, 1-28.
]Search in Google Scholar
[
[20] Youssef, K., Jarenwattananon, N.N., Bouchard, L. (2015). Feature-preserving noise removal. IEEE Transactions on Medical Imaging, 34, 1822-1829.10.1109/TMI.2015.240926525769149
]Search in Google Scholar
[
[21] Qiu, Z., Yang, L., Lu, W. (2011). A new featurepreserving nonlinear anisotropic diffusion method for image denoising. In BMVC 2011: The 22nd British Machine Vision Conference. BMVA, 1-11.
]Search in Google Scholar
[
[22] Li, Y., Jiang, M. (2018). Spatial-fractional order diffusion filtering. Journal of Mathematical Chemistry, 56, 257-267.10.1007/s10910-017-0795-z
]Search in Google Scholar
[
[23] Zhou, Q., Gao, J., Wang, Z., Li, K. (2016). Adaptive variable time fractional anisotropic diffusion filtering for seismic data noise attenuation. IEEE Transactions on Geoscience and Remote Sensing, 54, 1905-1917.10.1109/TGRS.2015.2490158
]Search in Google Scholar
[
[24] Li, Y., Liu, F., Turner, I.W., Li, T. (2018). Timefractional diffusion equation for signal smoothing. Applied Mathematics and Computation, 326, 108-116.10.1016/j.amc.2018.01.007
]Search in Google Scholar
[
[25] Cuesta, E., Kirane, M., Malik, S.A. (2012). Image structure preserving denoising using generalized fractional time integrals. Signal Processing, 92, 553-563.10.1016/j.sigpro.2011.09.001
]Search in Google Scholar
[
[26] Bai, J., Feng, X. (2007). Fractional-order anisotropic diffusion for image denoising. IEEE Transactions on Image Processing, 16, 2492-2502.10.1109/TIP.2007.904971
]Search in Google Scholar
[
[27] Janev, M., Pilipovic, S., Atanackovic, T.M., Obradovic, R., Ralevic, N.M. (2011). Fully fractional anisotropic diffusion for image denoising. Mathematical and Computer Modelling, 54, 729-741.10.1016/j.mcm.2011.03.017
]Search in Google Scholar
[
[28] Meerschaert, M.M., Benson, D.A., Scheffler, H.-P., Baeumer, B. (2002). Stochastic solution of space–time fractional diffusion equations. Physical Review E, 65, 1103-1106.10.1103/PhysRevE.65.04110312005802
]Search in Google Scholar
[
[29] Feng, L.B., Zhuang, P., Liu, F., Turner, I., Gu, Y.T. (2016). Finite element method for space-time fractional diffusion equation. Numerical Algorithms, 72, 749-767.10.1007/s11075-015-0065-8
]Search in Google Scholar
[
[30] Chen, Z.Q., Meerschaert, M.M., Nane, E. (2012). Space-time fractional diffusion on bounded domains. Journal of Mathematical Analysis and Applications, 393 (2), 479-488.10.1016/j.jmaa.2012.04.032
]Search in Google Scholar
[
[31] Azerad, P., Bouharguane, A., Crouzet, J. (2012). Simultaneous denoising and enhancement of signals by a fractal conservation law. Communications in Nonlinear Science and Numerical Simulation, 17 (2), 867-881.10.1016/j.cnsns.2011.07.001
]Search in Google Scholar
[
[32] Chan, R.H., Lanza, A., Morigi, S., Sgallari, F. (2013). An adaptive strategy for the restoration of textured images using fractional order regularization. Numerical Mathematics: Theory, Methods and Applications, 6, 276-296.10.4208/nmtma.2013.mssvm15
]Search in Google Scholar
[
[33] Savitzky, A., Golay, M.J.E. (1964). Smoothing and differentiation of data by simplified least squares procedures. Analytical Chemistry, 36 (8) 1627-1639.10.1021/ac60214a047
]Search in Google Scholar
[
[34] Krishnan, S.R., Seelamantula, C.S. (2013). On the selection of optimum Savitzky-Golay filters. IEEE Transactions on Signal Processing, 61 (2) 380-391.10.1109/TSP.2012.2225055
]Search in Google Scholar
[
[35] Eilers, P.H.C. (2003). A perfect smoother. Analytical Chemistry, 75, 3631-3636.10.1021/ac034173t14570219
]Search in Google Scholar
[
[36] Stickel, J.J. (2010). Data smoothing and numerical differentiation by a regularization method. Computers & Chemical Engineering, 34, 467-475.10.1016/j.compchemeng.2009.10.007
]Search in Google Scholar
[
[37] Yandell, B.S. (1989). Spline smoothing and nonparametric regression. Technometrics, 31, 379-380.10.1080/00401706.1989.10488561
]Search in Google Scholar
[
[38] Liu, B., Sera, Y., Matsubara, N., Otsuka, K., Terabe, S. (2003). Signal denoising and baseline correction by discrete wavelet transform for microchip capillary electrophoresis. Electrophoresis, 24 (18), 3260-3265.10.1002/elps.20030554814518054
]Search in Google Scholar
[
[39] Alsberg, B.K., Woodward, A.M., Winson, M.K., Rowland, J.J., Kell, D.B. (1997). Wavelet denoising of infrared spectra. Analyst, 122, 645-652.10.1039/a608255f
]Search in Google Scholar
[
[40] Yang, Q., Turner, I., Liu, F., Ilic, M. (2011). Novel numerical methods for solving the time-space fractional diffusion equation in two dimensions. SIAM Journal on Scientific Computing, 33, 1159-1180.10.1137/100800634
]Search in Google Scholar
[
[41] Momani, S., Odibat, Z. (2008). Numerical solutions of the space-time fractional advection-dispersion equation. Numerical Methods for Partial Differential Equations, 24 (6), 1416-1429.10.1002/num.20324
]Search in Google Scholar
[
[42] Guan, Q., Gunzburger, M. (2015). θ schemes for finite element discretization of the space-time fractional diffusion equations. Journal of Computational and Applied Mathematics, 288, 264-273.10.1016/j.cam.2015.04.032
]Search in Google Scholar
[
[43] Zhao, J., Xiao, J., Xu, Y. (2013). A finite element method for the multiterm time-space Riesz fractional advection-diffusion equations in finite domain. Abstract and Applied Analysis, 2013, 1-15.10.1155/2013/868035
]Search in Google Scholar
[
[44] Latifizadeh, H. (2010). Analytical solution of linear and non-linear space-time fractional reaction-diffusion equations. International Journal of Chemical Reactor Engineering, 8 (1).
]Search in Google Scholar
