Adaptive Total Variation Image Denoising and Restoration Based on the Quadratic Differential in the Local Coordinate System

GUO Yong-cai; PENG Lan-hui; GAO Chao

doi:10.3969/j.issn.1003-501x.2012.08.002

[1] Rosenfeld A, Kak A C. Digital picture processing [M]. New York：Academic Press, 1982.

[2] Perona P, Malik J. Scale-space and edge detection using anisotropic diffusion [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence(S0162-8828), 1990, 12(7)：629-639.

[3] Rudin L I, Osher S, Fatemi E. Nonlinear total variation based noise removal algorithms [J]. Physica D：Nonlinear Phenomena(S0167-2789), 1992, 60(1/4)：259-268.

[4] Song B. Topics in variational PDE image segmentation [D]. University of California Los Angeles, 2003.

[5] ZHANG Hong-yin, PEN Qi-zong. Adaptive image denoising model based on total variation [J]. Opto-Electronic Engineering, 2006, 33(3)：50-53.

[6] Blomgren P, Chan T F, Mulet P, et al. Total variation image restoration：numerical methods and extensions [C]// Proceedings International Conference on Image Processing, Oct 26-29, 1997, 3：384-387.

[7] Chan T, Marquina A, Mulet P. High-order total variation-based image restoration [J]. SIAM Journal on Scientific Computing(S1064-8275), 2000, 22：503.

[8] Chen Q, Montesinos P, Sun Q S, et al. Adaptive total variation denoising based on difference curvature [J]. Image and Vision Computing(S0262-8856), 2010, 28(3)：298-306.

[9] Hu J, Wang H. Adaptive total variation based on feature scale [J]. Trans. Eng. Comput. Technol(S1000-9000), 2005, V2： 245-248.

[10] Catté F, Lions P L, Morel J M, et al. Image selective smoothing and edge detection by nonlinear diffusion [J]. SIAM Journal on Numerical Analysis(S0036-1429), 1992, 29(1)：182-193.

[11] Luo H G, Zhu L M, Ding H. Coupled anisotropic diffusion for image selective smoothing [J]. Signal Processing(S1070-9908), 2006, 86(7)：1728-1736.

[12] Aubert G, Kornprobst P. Mathematical problems in image processing：partial differential equations and the calculus of variations [M]. Springer-Verlag New York Inc, 2006.

[13] Jaun A, Hedin J, Johnson T. Numerical methods for partial differential equations [D]. Swedish Netuniversity, 1999.

[14] Marquina A, Osher S. Explicit algorithms for a new time dependent model based on level set motion for nonlinear deblurring and noise removal [J]. SIAM Journal on Scientific Computing(S1064-8275), 2000, 22(4)：387-405.

[15] Chambolle A, Levine S E, Lucier B J. An upwind finite-difference method for total variation-based image smoothing [J]. SIAM J. Imaging Sci(S1936-4954), 2011, 4：277-299.