Restoration of blurred TV picture caused by uniform linear motion
Computer Vision, Graphics, and Image Processing
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
Iterative methods for total variation denoising
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
Matrix computations (3rd ed.)
A variable-penalty alternating directions method for convex optimization
Mathematical Programming: Series A and B
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
The Primal-Dual Active Set Strategy as a Semismooth Newton Method
SIAM Journal on Optimization
Modeling Textures with Total Variation Minimization and Oscillating Patterns in Image Processing
Journal of Scientific Computing
A Variational Approach to Remove Outliers and Impulse Noise
Journal of Mathematical Imaging and Vision
Dual Norms and Image Decomposition Models
International Journal of Computer Vision
Image Decomposition into a Bounded Variation Component and an Oscillating Component
Journal of Mathematical Imaging and Vision
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
Structure-Texture Image Decomposition--Modeling, Algorithms, and Parameter Selection
International Journal of Computer Vision
SIAM Journal on Scientific Computing
A descent method for structured monotone variational inequalities
Optimization Methods & Software
Efficient Schemes for Total Variation Minimization Under Constraints in Image Processing
SIAM Journal on Scientific Computing
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
Subspace Correction Methods for Total Variation and $\ell_1$-Minimization
SIAM Journal on Numerical Analysis
Deblurring Poissonian images by split Bregman techniques
Journal of Visual Communication and Image Representation
Total variation projection with first order schemes
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Operator Splittings, Bregman Methods and Frame Shrinkage in Image Processing
International Journal of Computer Vision
A computational algorithm for minimizing total variation in image restoration
IEEE Transactions on Image Processing
Image restoration subject to a total variation constraint
IEEE Transactions on Image Processing
Image decomposition via the combination of sparse representations and a variational approach
IEEE Transactions on Image Processing
Information Sciences: an International Journal
Solving Large-Scale Least Squares Semidefinite Programming by Alternating Direction Methods
SIAM Journal on Matrix Analysis and Applications
Recovering Low-Rank and Sparse Components of Matrices from Incomplete and Noisy Observations
SIAM Journal on Optimization
Inexact Alternating Direction Methods for Image Recovery
SIAM Journal on Scientific Computing
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
Foundations and Trends® in Machine Learning
Alternating Direction Method for Covariance Selection Models
Journal of Scientific Computing
On the $O(1/n)$ Convergence Rate of the Douglas-Rachford Alternating Direction Method
SIAM Journal on Numerical Analysis
An ADM-based splitting method for separable convex programming
Computational Optimization and Applications
A proximal parallel splitting method for minimizing sum of convex functions with linear constraints
Journal of Computational and Applied Mathematics
Homogeneous Penalizers and Constraints in Convex Image Restoration
Journal of Mathematical Imaging and Vision
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In this paper, we study alternating direction methods for solving constrained total-variation image restoration and reconstruction problems. Alternating direction methods can be implementable variants of the classical augmented Lagrangian method for optimization problems with separable structures and linear constraints. The proposed framework allows us to solve problems of image restoration, impulse noise removal, inpainting, and image cartoon+texture decomposition. As the constrained model is employed, we need only to input the noise level, and the estimation of the regularization parameter is not required in these imaging problems. Experimental results for such imaging problems are presented to illustrate the effectiveness of the proposed method. We show that the alternating direction method is very efficient for solving image restoration and reconstruction problems.