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
Convergence of an Iterative Method for Total Variation Denoising
SIAM Journal on Numerical Analysis
A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures
On the Convergence of the Lagged Diffusivity Fixed Point Method in Total Variation Image Restoration
SIAM Journal on Numerical Analysis
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Image Decomposition into a Bounded Variation Component and an Oscillating Component
Journal of Mathematical Imaging and Vision
Smooth minimization of non-smooth functions
Mathematical Programming: Series A and B
Second-order Cone Programming Methods for Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
Efficient Minimization Methods of Mixed l2-l1 and l1-l1 Norms for Image Restoration
SIAM Journal on Scientific Computing
Constrained and SNR-Based Solutions for TV-Hilbert Space Image Denoising
Journal of Mathematical Imaging and Vision
Journal of Mathematical Imaging and Vision
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)
On Semismooth Newton's Methods for Total Variation Minimization
Journal of Mathematical Imaging and Vision
A TV Based Restoration Model with Local Constraints
Journal of Scientific Computing
Convex Hodge Decomposition and Regularization of Image Flows
Journal of Mathematical Imaging and Vision
Projected Gradient Based Color Image Decomposition
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Efficient Schemes for Total Variation Minimization Under Constraints in Image Processing
SIAM Journal on Scientific Computing
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
Deterministic edge-preserving regularization in computed imaging
IEEE Transactions on Image Processing
Image restoration subject to a total variation constraint
IEEE Transactions on Image Processing
The Equivalence of Half-Quadratic Minimization and the Gradient Linearization Iteration
IEEE Transactions on Image Processing
A New TwIST: Two-Step Iterative Shrinkage/Thresholding Algorithms for Image Restoration
IEEE Transactions on Image Processing
Locally Parallel Textures Modeling with Adapted Hilbert Spaces
EMMCVPR '09 Proceedings of the 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Multiplicative Noise Removal Using L1 Fidelity on Frame Coefficients
Journal of Mathematical Imaging and Vision
Deblurring Poissonian images by split Bregman techniques
Journal of Visual Communication and Image Representation
Journal of Mathematical Imaging and Vision
A two-step model for image denoising using a duality strategy and surface fitting
Journal of Computational and Applied Mathematics
Variational method for super-resolution optical flow
Signal Processing
SIAM Journal on Imaging Sciences
Operator Splittings, Bregman Methods and Frame Shrinkage in Image Processing
International Journal of Computer Vision
NESTA: A Fast and Accurate First-Order Method for Sparse Recovery
SIAM Journal on Imaging Sciences
Locally Parallel Texture Modeling
SIAM Journal on Imaging Sciences
Total Variation as a Local Filter
SIAM Journal on Imaging Sciences
Augmented Lagrangian Method for Generalized TV-Stokes Model
Journal of Scientific Computing
Efficient minimization of the non-local potts model
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Dual Norm Based Iterative Methods for Image Restoration
Journal of Mathematical Imaging and Vision
Continuous Multiclass Labeling Approaches and Algorithms
SIAM Journal on Imaging Sciences
Lagrangian multipliers and split Bregman methods for minimization problems constrained on Sn-1
Journal of Visual Communication and Image Representation
Linear convergence analysis of the use of gradient projection methods on total variation problems
Computational Optimization and Applications
A fixed-point augmented Lagrangian method for total variation minimization problems
Journal of Visual Communication and Image Representation
A Variational Framework for Region-Based Segmentation Incorporating Physical Noise Models
Journal of Mathematical Imaging and Vision
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This paper deals with first-order numerical schemes for image restoration. These schemes rely on a duality-based algorithm proposed in 1979 by Bermùdez and Moreno. This is an old and forgotten algorithm that is revealed wider than recent schemes (such as the Chambolle projection algorithm) and able to improve contemporary schemes. Total variation regularization and smoothed total variation regularization are investigated. Algorithms are presented for such regularizations in image restoration. We prove the convergence of all the proposed schemes. We illustrate our study with numerous numerical examples. We make some comparisons with a class of efficient algorithms (proved to be optimal among first-order numerical schemes) recently introduced by Y. Nesterov.