SIAM Journal on Control and Optimization
Proximal minimization algorithm with D-functions
Journal of Optimization Theory and Applications
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
Nonlinear proximal point algorithms using Bregman functions, with applications to convex programming
Mathematics of Operations Research
Proximal Minimization Methods with Generalized Bregman Functions
SIAM Journal on Control and Optimization
Parallel Optimization: Theory, Algorithms and Applications
Parallel Optimization: Theory, Algorithms and Applications
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
Nonlocal Image and Movie Denoising
International Journal of Computer Vision
Some First-Order Algorithms for Total Variation Based Image Restoration
Journal of Mathematical Imaging and 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
Fast numerical algorithms for total variation based image restoration
Fast numerical algorithms for total variation based image restoration
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
Inpainting by Flexible Haar-Wavelet Shrinkage
SIAM Journal on Imaging Sciences
Removing Multiplicative Noise by Douglas-Rachford Splitting Methods
Journal of Mathematical Imaging and Vision
IEEE Transactions on Image Processing
Deblurring Poissonian images by split Bregman techniques
Journal of Visual Communication and Image Representation
Total variation restoration of speckled images using a split-Bregman algorithm
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
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
Restoration of images based on subspace optimization accelerating augmented Lagrangian approach
Journal of Computational and Applied Mathematics
SIAM Journal on Scientific Computing
Deconvolving Poissonian images by a novel hybrid variational model
Journal of Visual Communication and Image Representation
Inexact Alternating Direction Methods for Image Recovery
SIAM Journal on Scientific Computing
On vector and matrix median computation
Journal of Computational and Applied Mathematics
A Fast Fixed Point Algorithm for Total Variation Deblurring and Segmentation
Journal of Mathematical Imaging and Vision
Segmentation of images with separating layers by fuzzy c-means and convex optimization
Journal of Visual Communication and Image Representation
Journal of Mathematical Imaging and Vision
Lagrangian multipliers and split Bregman methods for minimization problems constrained on Sn-1
Journal of Visual Communication and Image Representation
Journal of Visual Communication and Image Representation
Computational Optimization and Applications
Journal of Scientific Computing
Coupling Image Restoration and Segmentation: A Generalized Linear Model/Bregman Perspective
International Journal of Computer Vision
Image Restoration via Tight Frame Regularization and Local Constraints
Journal of Scientific Computing
An effective dual method for multiplicative noise removal
Journal of Visual Communication and Image Representation
Homogeneous Penalizers and Constraints in Convex Image Restoration
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 examine the underlying structure of popular algorithms for variational methods used in image processing. We focus here on operator splittings and Bregman methods based on a unified approach via fixed point iterations and averaged operators. In particular, the recently proposed alternating split Bregman method can be interpreted from different points of view--as a Bregman, as an augmented Lagrangian and as a Douglas-Rachford splitting algorithm which is a classical operator splitting method. We also study similarities between this method and the forward-backward splitting method when applied to two frequently used models for image denoising which employ a Besov-norm and a total variation regularization term, respectively. In the first setting, we show that for a discretization based on Parseval frames the gradient descent reprojection and the alternating split Bregman algorithm are equivalent and turn out to be a frame shrinkage method. For the total variation regularizer, we also present a numerical comparison with multistep methods.