[1] Aubert, G., Vese, L.: A variational method in image recovery. SIAM J. Numer. Anal. 34, 1948-1979 (1997)
[2] Bae, E., Tai, X.C., Zhu, W.: Augmented Lagrangian method for an Euler’s elastica based segmentation model that promotes convex contours. Inverse Probl. Imag. 11, 1-23 (2017)
[3] Bellettini, G., Caselles, V., Novaga, M.: The total variation flow in \begin{document}$ {\mathbb{R} }^{n} $\end{document}. J. Differential Equations 184, 475-525 (2002)
[4] Benning, M., Burger, M.: Modern regularization methods for inverse problems. Acta Numerica 27, 1-111 (2018). https://doi.org/10.1017/S0962492918000016
[5] Bertalmio, M., Vese, L., Sapiro, G., Osher, S.: Simultaneous structure and texture image inpainting. IEEE Trans. Image Process. 12, 882-889 (2003)
[6] Bredies, K., Kunisch, K., Pock, T.: Total generalized variation. SIAM J. Imaging Sci. 3, 492-526 (2010)
[7] Brito-Loeza, C., Chen, K.: Multigrid algorithm for high order denoising. SIAM J. Imaging Sci. 3, 363-389 (2010)
[8] Chambolle, A., Lions, P.L.: Image recovery via total variation minimization and related problems. Numer. Math. 76, 167-188 (1997)
[9] Chambolle, A., Pock, T.: A first-order primal-dual algorithm for convex problems with applications to imaging. J. Math. Imaging Vis. 40, 120-145 (2011)
[10] Chan, T., Esedoglu, S.: Aspects of total variation regularized \begin{document}$ L^{1} $\end{document} function approximation. SIAM J. Appl. Math. 65, 1817-1837 (2005)
[11] Chan, T., Esedoglu, S., Park, F., Yip, M.H.: Recent developments in total variation image restoration. In: Paragios, N., Chen, Y., Faugeras, O. (eds.) Handbook of Mathematical Models in Computer Vision. Springer Verlag (2005)
[12] Chan, T., Marquina, A., Mulet, P.: High-order total variation-based image restoration. SIAM J. Sci. Comput. 22, 503-516 (2000)
[13] Chan, T., Shen, J.: Mathematical models for local nontexture inpaintings. SIAM J. Appl. Math. 62, 1019-1043 (2001)
[14] Chan, T., Wong, C.K.: Total variation blind deconvolution. IEEE Trans. Image Process. 7, 370-375 (1998)
[15] Chang, Q.S., Che, Z.Y.: An adaptive algorithm for TV-based model of three norms $L_q\left(q=\frac{1}{2}, 1,2\right)$ in image restoration. Appl. Math. Comput. 329, 251-265 (2018)
[16] Glowinski, R., Le Tallec, P.: Augmented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanics. SIAM, Philadelphia (1989)
[17] Goldstein, T., Osher, S.: The split Bregman method for L1-regularized problems. SIAM J. Imaging Sci. 2, 323-343 (2009)
[18] Lysaker, M., Lundervold, A., Tai, X.C.: Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time. IEEE. Trans. Image Process. 12, 1579-1590 (2003)
[19] Lysaker, M., Osher, S., Tai, X.C.: Noise removal using smoothed normals and surface fitting. IEEE. Trans. Image Process. 13, 1345-1457 (2004)
[20] Meyer, Y.: Oscillating Patterns in Image Processing and Nonlinear Evolution Equations. University Lecture Series, Vol. 22, Amer. Math. Soc. Providence, RI (2001)
[21] Mumford, D., Shah, J.: Optimal approximation by piecewise smooth functions and associated variational problems. Comm. Pure Appl. Math. 42, 577-685 (1989)
[22] Osher, S., Burger, M., Goldfarb, D., Xu, J.J., Yin, W.T.: An iterative regularization method for total variation-based image restoration. Multiscale Model. Simul. 4, 460-489 (2005)
[23] Osher, S., Sole, A., Vese, L.: Image decomposition and restoration using total variation minimization and the H-1norm. Multiscale Model. Simul. 1, 349-370 (2003)
[24] Papafitsoros, K., Schönlieb, C.B.: A combined first and second order variational approach for image reconstruction. J. Math. Imaging Vis. 48, 308-338 (2014). https://doi.org/10.1007/s10851-013-0445-4
[25] Rockafellar, R.T.: Augmented Lagrangians and applications of the proximal point algorithm in convex programming. Math. Oper. Res. 1, 97-116 (1976)
[26] Rudin, L., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithm. Phys. D 60, 259-268 (1992)
[27] Setzer, S., Steidl, G.: Variational methods with higher order derivatives in image processing. In: Approximation XII, pp. 360-386 (2008)
[28] Strong, D., Chan, T.: Edge-preserving and scale-dependent properties of total variation regularization. Inverse Problems 19, 165-187 (2003)
[29] Tai, X.C., Hahn, J., Chung, G.J.: A fast algorithm for Euler’s elastica model using augmented Lagrangian method. SIAM J. Imaging Sci. 4, 313-344 (2011)
[30] Vese, L.: A study in the BV space of a denoising-deblurring variational problem. Appl. Math. Optim. 44, 131-161 (2001)
[31] Wu, C., Tai, X.C.: Augmented Lagrangian method, dual methods, and split Bregman iteration for ROF, vectorial TV, and high order models. SIAM J. Imaging Sci. 3, 300-339 (2010)
[32] Yashtini, M., Kang, S.H., Zhu, W.: Efficient alternating minimization methods for variational edge-weighted colorization models. Adv. Comput. Math. 45, 1735-1767 (2019)
[33] Zhu, W.: A numerical study of a mean curvature denoising model using a novel augmented Lagrangian method. Inverse Probl. Imag. 11, 975-996 (2017)
[34] Zhu, W.: A first-order image denoising model for staircase reduction. Adv. Comput. Math. 45, 3217-3239 (2019)
[35] Zhu, W.: Image denoising using Lp-norm of mean curvature of image surface. J. Sci. Comput. 83, 32 (2020). https://doi.org/10.1007/s10915-020-01216-x
[36] Zhu, W.: A first-order image restoration model that promotes image contrast preservation. J. Sci. Comput. 88, 46 (2021). https://doi.org/10.1007/s10915-021-01557-1
[37] Zhu, W., Chan, T.: Image denoising using mean curvature of image surface. SIAM J. Imaging Sci. 5, 1-32 (2012)
[38] Zhu, W., Tai, X.C., Chan, T.: Augmented Lagrangian method for a mean curvature based image denoising model. Inverse Probl. Imag. 7, 1409-1432 (2013)
[39] Zhu, W., Tai, X.C., Chan, T.: Image segmentation using Euler’s elastica as the regularization. J. Sci. Comput. 57, 414-438 (2013)