Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Iterative methods for total variation denoising
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
Augmented Lagrangian methods for nonsmooth, convex optimization in Hilbert spaces
Nonlinear Analysis: Theory, Methods & Applications
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Journal of Mathematical Imaging and Vision
Iterative Image Restoration Combining Total Variation Minimization and a Second-Order Functional
International Journal of Computer Vision
Image restoration combining a total variational filter and a fourth-order filter
Journal of Visual Communication and Image Representation
Image decomposition combining staircase reduction and texture extraction
Journal of Visual Communication and Image Representation
Some First-Order Algorithms for Total Variation Based Image Restoration
Journal of Mathematical Imaging and Vision
Augmented Lagrangian Method, Dual Methods and Split Bregman Iteration for ROF Model
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
A New Alternating Minimization Algorithm for Total Variation Image Reconstruction
SIAM Journal on Imaging Sciences
Duality-based algorithms for total-variation-regularized image restoration
Computational Optimization and Applications
Total variation minimization and a class of binary MRF models
EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Fourth-order partial differential equations for noise removal
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Information Sciences: an International Journal
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Based on the augmented Lagrangian strategy, we construct a projected gradient algorithm for image restoration and texture extraction. The proposed algorithm is established on the basis of a mixed model which combines the Rudin-Osher-Fatemi (ROF) model with the Lysaker-Lundevold-Tai (LLT) model to reduce the staircase effect and blur phenomenons. The proof of the convergence of the proposed algorithm is provided. Moreover, we show that the dual methods based on convex analysis which have been proposed in some papers can be actually deduced from the augmented Lagrangian strategy. Some numerical examples are supplied to illustrate the efficiency of the proposed algorithm.