Minimization methods for non-differentiable functions
Minimization methods for non-differentiable functions
Matrix analysis
Parallel and distributed computation: numerical methods
Parallel and distributed computation: numerical methods
SIAM Journal on Control and Optimization
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 proximal-based decomposition method for convex minimization problems
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
Alternating Projection-Proximal Methods for Convex Programming and Variational Inequalities
SIAM Journal on Optimization
An Algorithm for Total Variation Minimization and Applications
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
SIAM Journal on Scientific Computing
Dual extrapolation and its applications to solving variational inequalities and related problems
Mathematical Programming: Series A and B
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
Efficient Schemes for Total Variation Minimization Under Constraints in Image Processing
SIAM Journal on Scientific Computing
Bregman Iterative Algorithms for $\ell_1$-Minimization with Applications to Compressed Sensing
SIAM Journal on Imaging Sciences
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
SIAM Journal on Imaging Sciences
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
SIAM Journal on Imaging Sciences
The Split Bregman Method for L1-Regularized Problems
SIAM Journal on Imaging Sciences
A New Alternating Minimization Algorithm for Total Variation Image Reconstruction
SIAM Journal on Imaging Sciences
An Efficient Primal-Dual Method for $L^1$TV Image Restoration
SIAM Journal on Imaging Sciences
IEEE Transactions on Image Processing
Duality-based algorithms for total-variation-regularized image restoration
Computational Optimization and Applications
A Unified Primal-Dual Algorithm Framework Based on Bregman Iteration
Journal of Scientific Computing
Bregmanized Nonlocal Regularization for Deconvolution and Sparse Reconstruction
SIAM Journal on Imaging Sciences
Nonlocal Discrete Regularization on Weighted Graphs: A Framework for Image and Manifold Processing
IEEE Transactions on Image Processing
Intermediate flow field filtering in energy based optic flow computations
EMMCVPR'11 Proceedings of the 8th international conference on Energy minimization methods in computer vision and pattern recognition
Inexact Alternating Direction Methods for Image Recovery
SIAM Journal on Scientific Computing
Weakly convex coupling continuous cuts and shape priors
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Completely Convex Formulation of the Chan-Vese Image Segmentation Model
International Journal of Computer Vision
Segmentation of images with separating layers by fuzzy c-means and convex optimization
Journal of Visual Communication and Image Representation
A New TV-Stokes Model with Augmented Lagrangian Method for Image Denoising and Deconvolution
Journal of Scientific Computing
An alternating direction method for finding Dantzig selectors
Computational Statistics & Data Analysis
Journal of Mathematical Imaging and Vision
SIAM Journal on Imaging Sciences
Fast Algorithms for Image Reconstruction with Application to Partially Parallel MR Imaging
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
Higher-Order TV Methods--Enhancement via Bregman Iteration
Journal of Scientific Computing
A class of quasi-variational inequalities for adaptive image denoising and decomposition
Computational Optimization and Applications
Journal of Mathematical Imaging and Vision
A fixed-point augmented Lagrangian method for total variation minimization problems
Journal of Visual Communication and Image Representation
An improved first-order primal-dual algorithm with a new correction step
Journal of Global Optimization
International Journal of Bioinformatics Research and Applications
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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We generalize the primal-dual hybrid gradient (PDHG) algorithm proposed by Zhu and Chan in [An Efficient Primal-Dual Hybrid Gradient Algorithm for Total Variation Image Restoration, CAM Report 08-34, UCLA, Los Angeles, CA, 2008] to a broader class of convex optimization problems. In addition, we survey several closely related methods and explain the connections to PDHG. We point out convergence results for a modified version of PDHG that has a similarly good empirical convergence rate for total variation (TV) minimization problems. We also prove a convergence result for PDHG applied to TV denoising with some restrictions on the PDHG step size parameters. We show how to interpret this special case as a projected averaged gradient method applied to the dual functional. We discuss the range of parameters for which these methods can be shown to converge. We also present some numerical comparisons of these algorithms applied to TV denoising, TV deblurring, and constrained $l_1$ minimization problems.