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 Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Convex Optimization
An Efficient TVL1 Algorithm for Deblurring Multichannel Images Corrupted by Impulsive Noise
SIAM Journal on Scientific Computing
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
IEEE Transactions on Image Processing
An efficient algorithm for a class of fused lasso problems
Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining
Foundations and Trends® in Machine Learning
Fast, robust total variation-based reconstruction of noisy, blurred images
IEEE Transactions on Image Processing
On the $O(1/n)$ Convergence Rate of the Douglas-Rachford Alternating Direction Method
SIAM Journal on Numerical Analysis
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Total variation (TV) regularization has important applications in signal processing including image denoising, image deblurring, and image reconstruction. A significant challenge in the practical use of TV regularization lies in the nondifferentiable convex optimization, which is difficult to solve especially for large-scale problems. In this paper, we propose an efficient alternating augmented Lagrangian method (ADMM) to solve total variation regularization problems. The proposed algorithm is applicable for tensors, thus it can solve multidimensional total variation regularization problems. One appealing feature of the proposed algorithm is that it does not need to solve a linear system of equations, which is often the most expensive part in previous ADMM-based methods. In addition, each step of the proposed algorithm involves a set of independent and smaller problems, which can be solved in parallel. Thus, the proposed algorithm scales to large size problems. Furthermore, the global convergence of the proposed algorithm is guaranteed, and the time complexity of the proposed algorithm is O(dN/ε) on a d-mode tensor with N entries for achieving an ε-optimal solution. Extensive experimental results demonstrate the superior performance of the proposed algorithm in comparison with current state-of-the-art methods.