Parallel and distributed computation: numerical methods
Parallel and distributed computation: numerical methods
Mathematical Programming: Series A and B
A globally convergent Newton method for solving strongly monotone variational inequalities
Mathematical Programming: Series A and B
A proximal-based decomposition method for convex minimization problems
Mathematical Programming: Series A and B
A variable-penalty alternating directions method for convex optimization
Mathematical Programming: Series A and B
Alternating Projection-Proximal Methods for Convex Programming and Variational Inequalities
SIAM Journal on Optimization
Journal of Optimization Theory and Applications
Iterative Methods for Toeplitz Systems (Numerical Mathematics and Scientific Computation)
Iterative Methods for Toeplitz Systems (Numerical Mathematics and Scientific Computation)
A descent method for structured monotone variational inequalities
Optimization Methods & Software
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
Deblurring Poissonian images by split Bregman techniques
Journal of Visual Communication and Image Representation
Multidimensional Systems and Signal Processing
SIAM Journal on Scientific Computing
Operator Splittings, Bregman Methods and Frame Shrinkage in Image Processing
International Journal of Computer Vision
SIAM Journal on Imaging Sciences
Alternating Direction Algorithms for $\ell_1$-Problems in Compressive Sensing
SIAM Journal on Scientific Computing
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
Alternating Direction Method for Image Inpainting in Wavelet Domains
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
An ADM-based splitting method for separable convex programming
Computational Optimization and Applications
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In the image processing community, there have recently been many restoration and reconstruction problems that can be reformulated into linearly constrained convex programming models whose objective functions have separable structures. These favorable reformulations have promoted impressive applications of the alternating direction method (ADM) in the field of image processing. At each iteration, the computation of ADM is dominated by solving two subproblems exactly. However, in many restoration and reconstruction applications, it is either impossible or extremely expensive to obtain exact solutions of these ADM subproblems. This fact urges the development on inexact versions of ADM, which allow the generated ADM subproblems to be solved approximately subject to certain inexactness criteria. In this paper, we develop some truly implementable inexact ADMs whose inexactness criteria controlling the accuracy of the ADM subproblems are easily implementable. The convergence of the new inexact ADMs will be proved. Numerical results on several image processing problems will be given to illustrate the effectiveness of the proposed inexact ADMs.