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
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
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Bregman Iterative Algorithms for $\ell_1$-Minimization with Applications to Compressed Sensing
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
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
Total-Variation Based Piecewise Affine Regularization
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Adaptive Variational Method for Restoring Color Images with High Density Impulse Noise
International Journal of Computer Vision
Geometric Applications of the Split Bregman Method: Segmentation and Surface Reconstruction
Journal of Scientific Computing
Fast image recovery using variable splitting and constrained optimization
IEEE Transactions on Image Processing
Fast and exact primal-dual iterations for variational problems in computer vision
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part II
Restoration of Poissonian images using alternating direction optimization
IEEE Transactions on Image Processing
Split Bregman method for large scale fused Lasso
Computational Statistics & Data Analysis
A unifying approach to isotropic and anisotropic total variation denoising models
Journal of Computational and Applied Mathematics
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
SIAM Journal on Imaging Sciences
Operator Splittings, Bregman Methods and Frame Shrinkage in Image Processing
International Journal of Computer Vision
Surface reconstruction using power watershed
ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
Wavelet frame based surface reconstruction from unorganized points
Journal of Computational Physics
A framework for intrinsic image processing on surfaces
Computer Vision and Image Understanding
SIAM Journal on Imaging Sciences
A Fast Algorithm for Euler's Elastica Model Using Augmented Lagrangian Method
SIAM Journal on Imaging Sciences
Alternating Direction Method for Image Inpainting in Wavelet Domains
SIAM Journal on Imaging Sciences
Augmented Lagrangian Method for Generalized TV-Stokes Model
Journal of Scientific Computing
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
A Variational Approach for Sharpening High Dimensional Images
SIAM Journal on Imaging Sciences
Continuous Multiclass Labeling Approaches and Algorithms
SIAM Journal on Imaging Sciences
Fast reduction of speckle noise in real ultrasound images
Signal Processing
X-Ray CT Image Reconstruction via Wavelet Frame Based Regularization and Radon Domain Inpainting
Journal of Scientific Computing
Bregmanized Domain Decomposition for Image Restoration
Journal of Scientific Computing
Tetrolet regularization and learning for single frame image super-resolution
IScIDE'12 Proceedings of the third Sino-foreign-interchange conference on Intelligent Science and Intelligent Data Engineering
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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We examine relations between popular variational methods in image processing and classical operator splitting methods in convex analysis. We focus on a gradient descent reprojection algorithm for image denoising and the recently proposed Split Bregman and alternating Split Bregman methods. By identifying the latter with the so-called Douglas-Rachford splitting algorithm we can guarantee its convergence. We show that for a special setting 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.