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Analysis of the TV regularization and $H^{1}$ fidelity model for decomposing animage into cartoon plus texture
1.  Department of Mathematics, University of Sussex, Brighton, BN1 9RF, United Kingdom, United Kingdom 
[1] 
John B. Greer, Andrea L. Bertozzi. $H^1$ Solutions of a class of fourth order nonlinear equations for image processing. Discrete & Continuous Dynamical Systems  A, 2004, 10 (1&2) : 349366. doi: 10.3934/dcds.2004.10.349 
[2] 
JianFeng Cai, Raymond H. Chan, Zuowei Shen. Simultaneous cartoon and texture inpainting. Inverse Problems & Imaging, 2010, 4 (3) : 379395. doi: 10.3934/ipi.2010.4.379 
[3] 
Feishe Chen, Lixin Shen, Yuesheng Xu, Xueying Zeng. The Moreau envelope approach for the L1/TV image denoising model. Inverse Problems & Imaging, 2014, 8 (1) : 5377. doi: 10.3934/ipi.2014.8.53 
[4] 
Changchun Liu. A fourth order nonlinear degenerate parabolic equation. Communications on Pure & Applied Analysis, 2008, 7 (3) : 617630. doi: 10.3934/cpaa.2008.7.617 
[5] 
José A. Carrillo, Ansgar Jüngel, Shaoqiang Tang. Positive entropic schemes for a nonlinear fourthorder parabolic equation. Discrete & Continuous Dynamical Systems  B, 2003, 3 (1) : 120. doi: 10.3934/dcdsb.2003.3.1 
[6] 
Luca Calatroni, Bertram Düring, CarolaBibiane Schönlieb. ADI splitting schemes for a fourthorder nonlinear partial differential equation from image processing. Discrete & Continuous Dynamical Systems  A, 2014, 34 (3) : 931957. doi: 10.3934/dcds.2014.34.931 
[7] 
Shi Yan, Jun Liu, Haiyang Huang, XueCheng Tai. A dual EM algorithm for TV regularized Gaussian mixture model in image segmentation. Inverse Problems & Imaging, 2019, 13 (3) : 653677. doi: 10.3934/ipi.2019030 
[8] 
Huafei Di, Yadong Shang, Xiaoxiao Zheng. Global wellposedness for a fourth order pseudoparabolic equation with memory and source terms. Discrete & Continuous Dynamical Systems  B, 2016, 21 (3) : 781801. doi: 10.3934/dcdsb.2016.21.781 
[9] 
Xu Liu, Jun Zhou. Initialboundary value problem for a fourthorder plate equation with HardyHénon potential and polynomial nonlinearity. Electronic Research Archive, 2020, 28 (2) : 599625. doi: 10.3934/era.2020032 
[10] 
Stephen C. Preston, Ralph Saxton. An $H^1$ model for inextensible strings. Discrete & Continuous Dynamical Systems  A, 2013, 33 (5) : 20652083. doi: 10.3934/dcds.2013.33.2065 
[11] 
Jianhong (Jackie) Shen, Sung Ha Kang. Quantum TV and applications in image processing. Inverse Problems & Imaging, 2007, 1 (3) : 557575. doi: 10.3934/ipi.2007.1.557 
[12] 
Zongming Guo, Long Wei. A fourth order elliptic equation with a singular nonlinearity. Communications on Pure & Applied Analysis, 2014, 13 (6) : 24932508. doi: 10.3934/cpaa.2014.13.2493 
[13] 
Zongming Guo, Long Wei. A perturbed fourth order elliptic equation with negative exponent. Discrete & Continuous Dynamical Systems  B, 2018, 23 (10) : 41874205. doi: 10.3934/dcdsb.2018132 
[14] 
Hayden Schaeffer, John Garnett, Luminita A. Vese. A texture model based on a concentration of measure. Inverse Problems & Imaging, 2013, 7 (3) : 927946. doi: 10.3934/ipi.2013.7.927 
[15] 
Amine Laghrib, Abdelkrim Chakib, Aissam Hadri, Abdelilah Hakim. A nonlinear fourthorder PDE for multiframe image superresolution enhancement. Discrete & Continuous Dynamical Systems  B, 2020, 25 (1) : 415442. doi: 10.3934/dcdsb.2019188 
[16] 
To Fu Ma. Positive solutions for a nonlocal fourth order equation of Kirchhoff type. Conference Publications, 2007, 2007 (Special) : 694703. doi: 10.3934/proc.2007.2007.694 
[17] 
Chunhua Jin, Jingxue Yin, Zejia Wang. Positive periodic solutions to a nonlinear fourthorder differential equation. Communications on Pure & Applied Analysis, 2008, 7 (5) : 12251235. doi: 10.3934/cpaa.2008.7.1225 
[18] 
Chuang Zheng. Inverse problems for the fourth order Schrödinger equation on a finite domain. Mathematical Control & Related Fields, 2015, 5 (1) : 177189. doi: 10.3934/mcrf.2015.5.177 
[19] 
Gang Meng. The optimal upper bound for the first eigenvalue of the fourth order equation. Discrete & Continuous Dynamical Systems  A, 2017, 37 (12) : 63696382. doi: 10.3934/dcds.2017276 
[20] 
M. Ben Ayed, K. El Mehdi, M. Hammami. Nonexistence of bounded energy solutions for a fourth order equation on thin annuli. Communications on Pure & Applied Analysis, 2004, 3 (4) : 557580. doi: 10.3934/cpaa.2004.3.557 
2018 Impact Factor: 0.925
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