[1] R. Aboulaich, S. Boujena, E. El Guarmah, A nonlinear parabolic model in processing of medical
image, Math. Model. Nat. Phenom. 6 (2008) 131–145.
[2] R. Aboulaich, D. Meskine, A. Souissi, New diffusion models in image processing, Comput. Math.
Appl. 56 (2008) 874–882.
[3] H. Antil, Z.W. Di, R. Khatri, Bilevel optimization, deep learning and fractional Laplacian regular-
ization with applications in tomography, Inverse Probl. 36 (2020) 064001.
[4] K. Bredies, K. Kunisch, T. Pock, Total generalized variation, SIAM J. Imaging Sci. 3 (2010) 492–
526.
[5] F. Catt, P.L. Lions, J.M. Morel, T. Coll, Image selective smoothing and edge detection by nonlinear
diffusion, SIAM J. Numer. Anal. 29 (1992) 182–193.
[6] C.C. Chang, H. Ju-Yuan, H. Chih-Ping, An adaptive median filter for image denoising, 2008 Sec-
ond International Symposium on Intelligent Information Technology Application, Shanghai, China,
(2008) 346-350.
[7] A. El Mourabit, I. El Mourabit, Adaptive nonlinear diffusion for image restoration via bilevel opti-
mization, Moroccan J. Pure Appl. Anal. 10 (2024) 220–235.
[8] I. El Mourabit, A. Laghrib, A. Hadri, A. Hakim, A theoretical study of a bilateral term with a
tensor-based fourth-order PDE for image super-resolution, Adv. Comput. Math. 48 (2022) 83.
[9] I. El Mourabit, M. El Rhabi, A. Hakim, A. Laghrib, E. Moreau, A new denoising model for multi-
frame super-resolution image reconstruction, Signal Process. 132 (2017) 51–65.
[10] D. Gabay, B. Mercier, A dual algorithm for the solution of nonlinear variational problems via finite
element approximation, Comput. Math. Appl. 2 (1976) 17–40.
[11] R. Glowinski, Y. Song, X. Yuan, An ADMM numerical approach to linear parabolic state con-
strained optimal control problems, Numer. Math. 144 (2020) 931–966.
[12] A. Hadri, A. Laghrib, and H. Oummi, An optimal variable exponent model for magnetic resonance
images denoising, Pattern Recognit. Lett. 151 (2021) 302–309.
[13] A. Hadri, A. Laghrib, I. El Mourabit, A new learning space-variant anisotropic constrained-PDE
for image denoising, Appl. Math. Model. 125 (2024) 139–163.
[14] N. Komodakis, J.-C. Pesquet, Playing with duality: An overview of recent primal-dual approaches
for solving large-scale optimization problems, IEEE Signal Process. Mag. 32 (2015) 31–54.
[15] A. Oulmelk, M. Srati, L. Afraites, Implementation of the ADMM approach to constrained optimal
control problem with a nonlinear time-fractional diffusion equation, Discrete Contin. Dyn. Syst.-S
18 (2022) 2238–2253.
[16] P. Perona, J. Malik, Scale-space and edge detection using anisotropic diffusion, IEEE Trans. Pattern
Anal. Mach. Intell. 12 (1990) 629–639.
[17] B.K. Shreyamsha Kumar, Image denoising based on Gaussian/bilateral filter and its method noise
thresholding, Signal Image Video Process. 7 (2013) 1159–1172.
[18] M. Wang, S. Zheng, X. Li, X. Qin, A new image denoising method based on Gaussian filter, 2014
International Conference on Information Science, Electronics and Electrical Engineering, Sapporo,
Japan, (2014)163-167.
[19] J. Weickert, Anisotropic Diffusion in Image Processing, Teuber Verlag, Stuttgart, 1998.
[20] J. Yang, X. Yuan, Linearized augmented Lagrangian and alternating direction methods for nuclear
norm minimization, Math. Comput. 82 (2013) 301–329.
[21] J. Zhang, R. Lai, C.C. J. Kuo, Adaptive directional total-variation model for latent fingerprint
segmentation, IEEE Trans. Inf. Forensics Security 8 (2013) 1261–1273.
)