[
[1] Aboulaich, Rajae, Driss Meskine, and Ali Souissi. “New diffusion models in image processing.” Computers & Mathematics with Applications 56.4 (2008): 874-882.10.1016/j.camwa.2008.01.017
]Search in Google Scholar
[
[2] Afraites, L., Atlas, A., Karami, F., & Meskine, D. (2016). Some class of parabolic systems applied to image processing. Discrete & Continuous Dynamical Systems-B, 21(6), 1671.10.3934/dcdsb.2016017
]Search in Google Scholar
[
[3] Afraites, L., Hadri, A., Laghrib, A., & Nachaoui, M. (2021). A weighted parameter identification PDE-constrained optimization for inverse image denoising problem. The Visual Computer, 1-16.10.3934/ipi.2022001
]Search in Google Scholar
[
[4] Bredies, Kristian, Karl Kunisch, and Thomas Pock. “Total generalized variation.” SIAM Journal on Imaging Sciences 3.3 (2010): 492-526.10.1137/090769521
]Search in Google Scholar
[
[5] Bergounioux, Ma¨ıtine, and Loic Piffet. “A second-order model for image denoising.” Set-Valued and Variational Analysis 18.3 (2010): 277-306.10.1007/s11228-010-0156-6
]Search in Google Scholar
[
[6] Bergounioux, M., & Piffet, L. (2010). A second-order model for image denoising. Set-Valued and Variational Analysis, 18(3), 277-306.10.1007/s11228-010-0156-6
]Search in Google Scholar
[
[7] Catté, F., Lions, P. L., Morel, J. M., & Coll, T. (1992). Image selective smoothing and edge detection by nonlinear diffusion. SIAM Journal on Numerical analysis, 29(1), 182-193.10.1137/0729012
]Search in Google Scholar
[
[8] J. C. De los Reyes, C.-B. Sch onlieb, T. Valkonen, Bilevel parameter learning for higher-order total variation regularisation models, Journal of Mathematical Imaging and Vision 57 (1) (2017) 1-25.10.1007/s10851-016-0662-8717560532355410
]Search in Google Scholar
[
[9] Elmahi, A., and D. Meskine. “Strongly nonlinear parabolic equations with natural growth terms in Orlicz spaces.” Nonlinear Analysis: Theory, Methods & Applications 60.1 (2005): 1-35.10.1016/j.na.2004.08.018
]Search in Google Scholar
[
[10] Elmahi, A., and D. Meskine. “Parabolic equations in Orlicz spaces.” Journal of the London Mathematical Society 72.2 (2005): 410-428.10.1112/S0024610705006630
]Search in Google Scholar
[
[11] El Mourabit, I., El Rhabi, M., Hakim, A., Laghrib, A., & Moreau, E. (2017). A new denoising model for multi-frame super-resolution image reconstruction. Signal Processinknog, 132, 51-65.10.1016/j.sigpro.2016.09.014
]Search in Google Scholar
[
[12] S. Farsiu, D. Robinson, M. Elad, P. Milanfar, Advances and challenges in super-resolution, Interna-tional Journal of Imaging Systems and Technology 14 (2) (2004) 47-57.10.1002/ima.20007
]Search in Google Scholar
[
[13] Michael Hintermüller, Kostas Papafitsoros, Carlos N. Rautenberg & Hongpeng Sun (2022) Dualization and Automatic Distributed Parameter Selection of Total Generalized Variation via Bilevel Optimization, Numerical Functional Analysis and Optimization, 43:8, 887-932.10.1080/01630563.2022.2069812
]Search in Google Scholar
[
[14] Hintermüller, Michael, and Carlos N. Rautenberg. “Optimal selection of the regularization function in a weighted total variation model. Part I: Modelling and theory.” Journal of Mathematical Imaging and Vision 59.3 (2017): 498-514.10.1007/s10851-017-0744-2
]Search in Google Scholar
[
[15] M. Hinterm uller, C. N. Rautenberg, T. Wu, A. Langer, Optimal selection of the regularization function in a weighted total variation model. part ii: Algorithm, its analysis and numerical tests, Journal of Mathematical Imaging and Vision 59 (3) (2017) 515-533.10.1007/s10851-017-0736-2
]Search in Google Scholar
[
[16] JAIN, Anil K. Fundamentals of digital image processing. Prentice-Hall, Inc., 1989.
]Search in Google Scholar
[
[17] A. Lanza, S. Morigi, F. Sgallari, Constrained TVp-l2 model for image restoration, Journal of Scientific. Computing 68 (1) (2016) 64-91.10.1007/s10915-015-0129-x
]Search in Google Scholar
[
[18] Nocedal, Jorge, and Stephen J. Wright, eds. Numerical optimization. New York, NY: Springer New York, 1999.10.1007/b98874
]Search in Google Scholar
[
[19] Perona, P., & Malik, J. (1990). Scale-space and edge detection using anisotropic diffusion. IEEE Transactions on pattern analysis and machine intelligence, 12(7), 629-639.10.1109/34.56205
]Search in Google Scholar
[
[20] Rudin, Leonid I., Stanley Osher, and Emad Fatemi. “Nonlinear total variation based noise removal algorithms.”Physica D: nonlinear phenomena 60.1-4 (1992): 259-268.10.1016/0167-2789(92)90242-F
]Search in Google Scholar
[
[21] Lv, X. G., Song, Y. Z., Wang, S. X., & Le, J. (2013). Image restoration with a high-order total variation minimization method. Applied Mathematical Modelling, 37(16-17), 8210-8224.10.1016/j.apm.2013.03.028
]Search in Google Scholar
[
[22] Tröltzsch, Fredi. Optimal control of partial differential equations: theory, methods, and applications. Vol. 112. American Mathematical Soc., 2010.10.1090/gsm/112/07
]Search in Google Scholar
[
[23] C. Van Chung, J. De los Reyes, C. Sch onlieb, Learning optimal spatially-dependent regularization parameters in total variation image denoising, Inverse Problems 33 (7) (2017) 074005.10.1088/1361-6420/33/7/074005
]Search in Google Scholar
[
[24] Yaroslavsky, L. P. (2012). Digital picture processing: an introduction (Vol. 9). Springer Science & Business Media.
]Search in Google Scholar
[
[25] Zhang, J., & Chen, K. (2015). A total fractional-order variation model for image restoration with nonhomogeneous boundary conditions and its numerical solution. SIAM Journal on Imaging Sciences, 8(4), 2487-2518.10.1137/14097121X
]Search in Google Scholar
