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
An efficient algorithm for image segmentation, Markov random fields and related problems
Journal of the ACM (JACM)
Practical Aspects of the Moreau--Yosida Regularization: Theoretical Preliminaries
SIAM Journal on Optimization
Analysis of iterative methods for saddle point problems: a unified approach
Mathematics of Computation
Texture Synthesis by Non-Parametric Sampling
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Non-local Regularization of Inverse Problems
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part III
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
A Variational Framework for Non-local Image Inpainting
EMMCVPR '09 Proceedings of the 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Fixed-Point Continuation for $\ell_1$-Minimization: Methodology and Convergence
SIAM Journal on Optimization
Bregman Iterative Algorithms for $\ell_1$-Minimization with Applications to Compressed Sensing
SIAM Journal on Imaging Sciences
Linearized Bregman Iterations for Frame-Based Image Deblurring
SIAM Journal on Imaging Sciences
The Split Bregman Method for L1-Regularized Problems
SIAM Journal on Imaging Sciences
Image Recovery via Nonlocal Operators
Journal of Scientific Computing
Iterated nonlocal means for texture restoration
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Regularization on discrete spaces
PR'05 Proceedings of the 27th DAGM conference on Pattern Recognition
Exact optimization of discrete constrained total variation minimization problems
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation
IEEE Transactions on Signal Processing
IEEE Transactions on Information Theory
An EM algorithm for wavelet-based image restoration
IEEE Transactions on Image Processing
The contourlet transform: an efficient directional multiresolution image representation
IEEE Transactions on Image Processing
Nonlocal Discrete Regularization on Weighted Graphs: A Framework for Image and Manifold Processing
IEEE Transactions on Image Processing
Split Bregman method for large scale fused Lasso
Computational Statistics & Data Analysis
SIAM Journal on Imaging Sciences
Wavelet frame based surface reconstruction from unorganized points
Journal of Computational Physics
SIAM Journal on Imaging Sciences
Analysis and Generalizations of the Linearized Bregman Method
SIAM Journal on Imaging Sciences
SIAM Journal on Imaging Sciences
Alternating Direction Method for Image Inpainting in Wavelet Domains
SIAM Journal on Imaging Sciences
Combinatorial Continuous Maximum Flow
SIAM Journal on Imaging Sciences
A statistical multiresolution strategy for image reconstruction
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
How to Compare Noisy Patches? Patch Similarity Beyond Gaussian Noise
International Journal of Computer Vision
A Nonlocal Version of the Osher-Solé-Vese Model
Journal of Mathematical Imaging and Vision
On the $O(1/n)$ Convergence Rate of the Douglas-Rachford Alternating Direction Method
SIAM Journal on Numerical Analysis
Fast Algorithms for Image Reconstruction with Application to Partially Parallel MR Imaging
SIAM Journal on Imaging Sciences
X-Ray CT Image Reconstruction via Wavelet Frame Based Regularization and Radon Domain Inpainting
Journal of Scientific Computing
An Efficient Algorithm for l0 Minimization in Wavelet Frame Based Image Restoration
Journal of Scientific Computing
Bregmanized Domain Decomposition for Image Restoration
Journal of Scientific Computing
Bregman operator splitting with variable stepsize for total variation image reconstruction
Computational Optimization and Applications
Fast two-stage segmentation via non-local active contours in multiscale texture feature space
Pattern Recognition Letters
Journal of Mathematical Imaging and Vision
A learning-based method for compressive image recovery
Journal of Visual Communication and Image Representation
A fixed-point augmented Lagrangian method for total variation minimization problems
Journal of Visual Communication and Image Representation
A New Nonlocal H1 Model for Image Denoising
Journal of Mathematical Imaging and Vision
Original Article: A new nonlocal total variation regularization algorithm for image denoising
Mathematics and Computers in Simulation
A boundary condition based deconvolution framework for image deblurring
Journal of Computational and Applied Mathematics
A Framework for Moving Least Squares Method with Total Variation Minimizing Regularization
Journal of Mathematical Imaging and Vision
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Bregman methods introduced in [S. Osher, M. Burger, D. Goldfarb, J. Xu, and W. Yin, Multiscale Model. Simul., 4 (2005), pp. 460-489] to image processing are demonstrated to be an efficient optimization method for solving sparse reconstruction with convex functionals, such as the $\ell^1$ norm and total variation [W. Yin, S. Osher, D. Goldfarb, and J. Darbon, SIAM J. Imaging Sci., 1 (2008), pp. 143-168; T. Goldstein and S. Osher, SIAM J. Imaging Sci., 2 (2009), pp. 323-343]. In particular, the efficiency of this method relies on the performance of inner solvers for the resulting subproblems. In this paper, we propose a general algorithm framework for inverse problem regularization with a single forward-backward operator splitting step [P. L. Combettes and V. R. Wajs, Multiscale Model. Simul., 4 (2005), pp. 1168-1200], which is used to solve the subproblems of the Bregman iteration. We prove that the proposed algorithm, namely, Bregmanized operator splitting (BOS), converges without fully solving the subproblems. Furthermore, we apply the BOS algorithm and a preconditioned one for solving inverse problems with nonlocal functionals. Our numerical results on deconvolution and compressive sensing illustrate the performance of nonlocal total variation regularization under the proposed algorithm framework, compared to other regularization techniques such as the standard total variation method and the wavelet-based regularization method.