Primal-Dual Decomposition by Operator Splitting and Applications to Image Deblurring ∗

作者: Daniel O'Connor , Lieven Vandenberghe

DOI: 10.1137/13094671X

关键词: Convex optimizationDecomposition (computer science)MathematicsMathematical optimizationOperator (computer programming)Image (mathematics)DeblurringApplied mathematicsSimple (abstract algebra)Regular polygonBoundary value problem

摘要: … The operators we will encounter in this paper are combinations of two elementary types of maximal monotone operators. The first is the subdifferential ∂f of a closed convex function f …

参考文章(68)
James G. Nagy, Dianne P. O'Leary, Restoring images degraded by spatially-variant blur SIAM Journal on Scientific Computing. ,vol. 19, pp. 1063- 1082 ,(1998) , 10.1137/S106482759528507X
Gitta Kutyniok, Morteza Shahram, Xiaosheng Zhuang, ShearLab: A Rational Design of a Digital Parabolic Scaling Algorithm Siam Journal on Imaging Sciences. ,vol. 5, pp. 1291- 1332 ,(2012) , 10.1137/110854497
Tony F. Chan, Gene H. Golub, Pep Mulet, A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration SIAM Journal on Scientific Computing. ,vol. 20, pp. 1964- 1977 ,(1999) , 10.1137/S1064827596299767
Jonathan E. Spingarn, Applications of the method of partial inverses to convex programming: Decomposition Mathematical Programming. ,vol. 32, pp. 199- 223 ,(1985) , 10.1007/BF01586091
Neel Joshi, Sing Bing Kang, C. Lawrence Zitnick, Richard Szeliski, Image deblurring using inertial measurement sensors international conference on computer graphics and interactive techniques. ,vol. 29, pp. 30- ,(2010) , 10.1145/1778765.1778767
Saima Ben Hadj, Laure Blanc-Féraud, Gilles Aubert, Space Variant Blind Image Restoration Siam Journal on Imaging Sciences. ,vol. 7, pp. 2196- 2225 ,(2014) , 10.1137/130945776
Laurent Condat, A primal-dual splitting method for convex optimization involving Lipschitzian, proximable and linear composite terms Journal of Optimization Theory and Applications. ,vol. 158, pp. 460- 479 ,(2013) , 10.1007/S10957-012-0245-9
Patrick L. Combettes, Valérie R. Wajs, SIGNAL RECOVERY BY PROXIMAL FORWARD-BACKWARD SPLITTING ∗ Multiscale Modeling & Simulation. ,vol. 4, pp. 1168- 1200 ,(2005) , 10.1137/050626090
Patrick L. Combettes, Jean-Christophe Pesquet, Primal-Dual Splitting Algorithm for Solving Inclusions with Mixtures of Composite, Lipschitzian, and Parallel-Sum Type Monotone Operators Set-valued and Variational Analysis. ,vol. 20, pp. 307- 330 ,(2012) , 10.1007/S11228-011-0191-Y
L. Denis, E. Thiebaut, F. Soulez, Fast model of space-variant blurring and its application to deconvolution in astronomy 2011 18th IEEE International Conference on Image Processing. pp. 2817- 2820 ,(2011) , 10.1109/ICIP.2011.6116257