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
Mathematical Programming: Series A and B
A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
Convex analysis and variational problems
Convex analysis and variational problems
Parallel and Distributed Computation: Numerical Methods
Parallel and Distributed Computation: Numerical Methods
High-Order Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Iterative Image Restoration Combining Total Variation Minimization and a Second-Order Functional
International Journal of Computer Vision
Enhancement of Blurred and Noisy Images Based on an Original Variant of the Total Variation
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Split Bregman Algorithm, Douglas-Rachford Splitting and Frame Shrinkage
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer 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
Bregman Iterative Algorithms for $\ell_1$-Minimization with Applications to Compressed Sensing
SIAM Journal on Imaging Sciences
The Split Bregman Method for L1-Regularized Problems
SIAM Journal on Imaging Sciences
A Fast Algorithm for Edge-Preserving Variational Multichannel Image Restoration
SIAM Journal on Imaging Sciences
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
Bregmanized Nonlocal Regularization for Deconvolution and Sparse Reconstruction
SIAM Journal on Imaging Sciences
De-noising by soft-thresholding
IEEE Transactions on Information Theory
Behavioral analysis of anisotropic diffusion in image processing
IEEE Transactions on Image Processing
Anisotropic diffusion of multivalued images with applications to color filtering
IEEE Transactions on Image Processing
Color TV: total variation methods for restoration of vector-valued images
IEEE Transactions on Image Processing
Fourth-order partial differential equations for noise removal
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
The staircasing effect in neighborhood filters and its solution
IEEE Transactions on Image Processing
Split Bregman method for large scale fused Lasso
Computational Statistics & Data Analysis
A framework for intrinsic image processing on surfaces
Computer Vision and Image Understanding
Geometry of total variation regularized Lp-model
Journal of Computational and Applied Mathematics
Homotopy method for a mean curvature-based denoising model
Applied Numerical Mathematics
Journal of Scientific Computing
Augmented Lagrangian Method for Generalized TV-Stokes Model
Journal of Scientific Computing
Domain decomposition methods with graph cuts algorithms for total variation minimization
Advances in Computational Mathematics
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
A New TV-Stokes Model with Augmented Lagrangian Method for Image Denoising and Deconvolution
Journal of Scientific Computing
A convex relaxation method for computing exact global solutions for multiplicative noise removal
Journal of Computational and Applied Mathematics
Fast regularization of matrix-valued images
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part III
IScIDE'12 Proceedings of the third Sino-foreign-interchange conference on Intelligent Science and Intelligent Data Engineering
Non-convex hybrid total variation for image denoising
Journal of Visual Communication and Image Representation
Variational structure-texture image decomposition on manifolds
Signal Processing
Journal of Scientific Computing
A fixed-point augmented Lagrangian method for total variation minimization problems
Journal of Visual Communication and Image Representation
Image Segmentation Using Euler's Elastica as the Regularization
Journal of Scientific Computing
Image Restoration via Tight Frame Regularization and Local Constraints
Journal of Scientific Computing
A coupled variational model for image denoising using a duality strategy and split Bregman
Multidimensional Systems and Signal Processing
A Combined First and Second Order Variational Approach for Image Reconstruction
Journal of Mathematical Imaging and Vision
A Framework for Moving Least Squares Method with Total Variation Minimizing Regularization
Journal of Mathematical Imaging and Vision
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In image processing, the Rudin-Osher-Fatemi (ROF) model [L. Rudin, S. Osher, and E. Fatemi, Phys. D, 60 (1992), pp. 259-268] based on total variation (TV) minimization has proven to be very useful. So far many researchers have contributed to designing fast numerical schemes and overcoming the nondifferentiability of the model. Methods considered to be particularly efficient for the ROF model include the Chan-Golub-Mulet (CGM) primal-dual method [T.F. Chan, G.H. Golub, and P. Mulet, SIAM J. Sci. Comput., 20 (1999), pp. 1964-1977], Chambolle's dual method [A. Chambolle, J. Math. Imaging Vis., 20 (2004), pp. 89-97], the splitting and quadratic penalty-based method [Y. Wang, J. Yang, W. Yin, and Y. Zhang, SIAM J. Imaging Sci., 1 (2008), pp. 248-272], and the split Bregman iteration [T. Goldstein and S. Osher, SIAM J. Imaging Sci., 2 (2009), pp. 323-343], as well as the augmented Lagrangian method [X.C. Tai and C. Wu, Lecture Notes in Comput. Sci. 5567, Springer-Verlag, Berlin, 2009, pp. 502-513]. In this paper, we first review the augmented Lagrangian method for the ROF model and then provide some convergence analysis and extensions to vectorial TV and high order models. All the algorithms and analysis will be presented in the discrete setting, which is much clearer for practical implementation than the continuous setting as in Tai and Wu, above. We also present, in the discrete setting, the connections between the augmented Lagrangian method, the dual methods, and the split Bregman iteration. Using our extensions and observations, we can easily figure out CGM and the split Bregman iteration for vectorial TV and high order models, which, to the best of our knowledge, have not been presented in the literature. Numerical examples demonstrate the efficiency and accuracy of our method, especially in the image deblurring case.